You flip a coin and then roll a 6-sided number cube (a die).
a. When finding the probability, does it matter whether you roll the die or flip the coin first?
b. Is there more than one way to draw a tree diagram for this problem? If so, does that change the likelihood that any outcome will occur?
c. Draw the shape of the tree diagram that you would use.
d. How many outcomes are there? List them.
e. Find the probability of rolling an even number and getting heads.
Answers
Answer:
a) No, it does not matter whether you roll the die or flip the coin first, as these two events are independent of each other, which means they do not affect each other.
b) Yes.
Let event 1 be flipping a coin and event 2 be rolling a die.Let event 1 be rolling a die and event 2 be flipping a coin.The likelihood that any outcome will occur will not change, as the events are independent.
c) see attached
d) 12 outcomes (H = head, T = tail, numbers represent the value of the die)
H 1 T 1
H 2 T 2
H 3 T 3
H 4 T 4
H 5 T 5
H 6 T 6
e)
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf P(even)=\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{1}{2}[/tex]
[tex]\implies \sf P(head)=\dfrac{1}{2}[/tex]
[tex]\implies \sf P(even)\:and\:P(head)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}[/tex]
Related Questions
An aircraft is timetabled to travel from A to B. Due to bad weather it flies from A to C then from C to B, where AC and CB make angles of 27° and 66° respectively with AB. If |AC| = 220 km, calculate |AB|.
Answers
Answer:
|AB| = 240 km
Step-by-step explanation:
Finding ∠C :
⇒ 27° + 66° + ∠C = 180°
⇒ ∠C = 180° - 93°
⇒ ∠C = 87°
Applying the Law of Sines :
⇒ sin 66° / 220 = sin 87° / AB
⇒ 0.913545458 / 220 = 0.998629535 / AB
⇒ AB = 220/0.913545458 x 0.998629535
⇒ AB = 240.819981 x 0.998629535
⇒ AB = 240.489946
⇒ |AB| = 240 km (nearest whole kilometer)
Answer:
|AB| = 240 km (nearest km)
Step-by-step explanation:
Draw a sketch with the given information (attached).
Calculate the missing angle (shown in red on the attached diagram).
Given:
∠CAB = 27°∠CBA = 66°The interior angles of a triangle sum to 180°
⇒ ∠ACB + ∠CAB + ∠CBA = 180°
⇒ ∠ACB + 27° + 66° = 180°
⇒ ∠ACB = 180° - 27° - 66°
⇒ ∠ACB = 87°
Use Sine Rule for sides to calculate |AB|:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \sf \dfrac{|AB|}{\sin ACB}=\dfrac{|AC|}{\sin CBA}[/tex]
[tex]\implies \sf \dfrac{|AB|}{\sin (87^{\circ})}=\dfrac{220}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=\dfrac{220\:\sin (87^{\circ})}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=240.4899459...[/tex]
[tex]\implies \sf |AB|=240\:km\:(nearest\:km)[/tex]
If P is directly proportional to Q. And Q = 30 when P = 40. Find Q when P = 70
Answers
Answer:
Q = 52.5
Step-by-step explanation:
given P is directly proportional to Q then the equation relating them is
P = kQ ← k is the constant of proportion
to find k use the condition Q = 30 when P = 40 , then
40 = 30k ( divide both sides by 30 )
[tex]\frac{40}{30}[/tex] = [tex]\frac{4}{3}[/tex] = k
P = [tex]\frac{4}{3}[/tex] Q ← equation of proportion
when P = 70 , then
70 = [tex]\frac{4}{3}[/tex] Q ( multiply both sides by 3 to clear the fraction )
210 = 4Q ( divide both sides by 4 )
52.5 = Q
Proving Parallelogram
Answers
Answer:
Soln.
Given that we have proven:AB =CD and BC=DA
we will be said that the A and C is the angle of 90° and we will add the letters to get the results so let's started the A+90°+ 90°+ B+C+ D=90°
A+180°+B+C+D
180°+90°
=270°
8th grade distributive property equations and solutions
Answers
The value of x will be given as for the given expression X = -1
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
2x + 12 = 10
2x = 10 - 12
2x = -2
x = -1
first you distribute 2 to x and 6 which equals 2x+12=10 then you subtract 12 from 10 which equals 2x=-2 then divide -2 by 2x to see what x equals so x=-1
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V
Write 8.4% as a fraction in simplest form.
Answers
Answer:
21/250
Step-by-step explanation:
Converting percentage to fraction :
Divide by 100%8.4%/100%8.4/100Multiply both sides by 10 to remove the decimal8.4 x 10 / 100 x 1084/1000Divide both sides by 4(84/4)/(1000/4)21/250Madison is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with three equal-sized sections labeled Walk, Run, Stop and spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange?
Answers
Answer:
12.
Step-by-step explanation:
There are 3 * 4 = 12 possible outcomes
for example
Walk / Red
Walk/Green
Walk/Blue
Walk/Orange
- and there are 4 similar outcomes for Run and Stop.
How much water should be added to 22 ml of 12% alcohol solution to reduce the concentration to 11%
Answers
The amount of water that is needed to be added to the 12% concentration solution to make it 11% concentrated is 2 ml.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that the alcohol solution of 22 ml has a 12% of concentration. Therefore, the amount of alcohol in the solution is,
12% of 22ml = 2.64ml
Since the amount of alcohol should be the same while the concentration should be diluted, therefore, the amount of alcohol in the final solution can be written as,
[tex]11\%\ of\ x = 2.64{\rm\ ml}\\\\\dfrac{11}{100} \times x = 2.64\\\\x = 24\rm\ ml[/tex]
As the total solution with 12% concentration was 22 ml, while the total solution with 11% concentration was 24 ml.
Hence, the amount of water that is needed to be added to the 12% concentration solution to make it 11% concentrated is 2 ml.
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A. 23.7
B. 11.2
C. 9.5
D. 57.3
E. 30.0
F. 6.0
Answers
Answer:
c.9.5
Step-by-step explanation:
im awesome so so very
At what nominal rate, compounded semi-annual, would $6,000.00 have to be invested to amount to
$9,066.41 in 6 years?
The rate would be
%. (If needed, round to 1 decimal place.)
Answers
Question: How many miles can we paddle in 1 hour at the Los Angeles river?
The river is going at 25 mph
and you are paddling at a consistent rate
Answers
Answer:
125 mph
Step-by-step explanation:
The river is going 25 mph every 20 minutes
[tex]20[/tex] [tex]minutes=25[/tex][tex]40[/tex] [tex]minutes=50[/tex][tex]60[/tex] [tex]minutes=75[/tex] [tex]80[/tex] [tex]minutes =100[/tex][tex]1[/tex] [tex]hour = 125[/tex]Therefore we can paddle 125 miles at consistent rate.
What is the probability that a patient shows improvement
if it is known that the patient was given the drug?
Answers
Answer:
.3375
Explanation:
Total people who were given drug: 800
Total people who showed improvement: 270
Probability:
[tex]\boxed{ \sf \dfrac{favorable \ outcomes }{total \ possible \ outcomes}}[/tex]
insert values
[tex]\rightarrow \sf \dfrac{270}{800}[/tex]
simplify
[tex]\rightarrow \sf \dfrac{27}{80}[/tex]
in decimals
[tex]\rightarrow \sf 0.3375[/tex]
Answer:
d) .3375Step-by-step explanation:
let E be the event : “the patient shows improvement”
D be the event : “the patient was given the drug”
here we are in a conditional probability situation:
Let E/D be the event “a patient shows improvement ,if it is known that the patient was given the drug”
[tex]p\left( E|D\right) =\frac{p\left( E\cap D\right) }{p\left( D\right) }[/tex]
[tex]=\frac{270}{800}[/tex]
[tex]=0.3375[/tex]
about 1 2 of the population has red hair if 800 people were ramdomly sampled about how many of them would you expect to be read heads
Answers
Answer:
10-12
Step-by-step explanation:
1.5% of 800 is 12
Determine the consumers’ surplus of the market price is set at the equilibrium price (remember that x is measured in thousands)
Answers
Answer:here the answer
Step-by-step explanation:
....
Marci needs to rent a storage. She needs to determine the volume of the storage unit. If the storage unit is 8 feet high, what is the volume of the storage unit
Answers
First off, you only need one side to determine volume.
Volume = length x width x height.
Currently we know: volume = ? x ? x 8ft
Lets make an inference that the the storage is completely symmetrical, all sides even. That’d leave us with: volume = 8 x 8 x 8 which is also 8^3. With that being said, the volume of the storage unit is 512.
−8 ≤ −3; Add 11 to both sides
The resulting inequality is:
Answers
Answer:
True, (-∞, ∞) 3 ≤ 8
Step-by-step explanation:
−8 + 11 ≤ −3 + 11
3 ≤ 8
Mya bought x shirts for $14.50 each and used a $20 coupon. Which equation represents theh total amount, a, she spent?
Answers
Also it would be 14x - 20
If there’s an answer that looked like that then that probably it.
exam tomorrow need help
Answers
Answer:
See below ~
Step-by-step explanation:
The perimeter of a figure refers to the sum of the side lengths of its edges.
Figure (a) : Triangle
⇒ P = 2a + 1 + 3a + a - 4
⇒ P = 6a - 3
⇒ P = 3 (2a - 1)
Figure (b) : Hexagon
⇒ P = 3m - 1 + 3n + n + m + 3m + 1 + 4n + m + n + 2
⇒ P = 3m + m + 3m + m + 3n + n + 4n + n + 1 - 1 + 2
⇒ P = 8m + 9n + 2
Figure (c) : Trapezoid
⇒ P = 2a + 3 + 3a - b + 2a + 2b - 4 + b + 4
⇒ P = 2a + 3a + 2a + 2b + b - b + 4 - 4 + 3
⇒ P = 7a + 2b + 3
the table represent a function? Why or why not?
A. Yes, because every x-value corresponds to exactly one y-value.
B. No, because the y-values are positive.
C. Yes, because there are different y-values.
D. No, because one x-value corresponds to two different y-values.
Answers
Answer:
D is the answer I'm pretty sure
Step-by-step explanation:
6 has to y values
hhelp plssssssssssssssssssssssssssss
Answers
Answer:
This is false
Step-by-step explanation:
a bottle contains 2 1/2 cups of apple juice a serving of apple juice is 1/2 cup how many servings does the bottle contain
Answers
By applying aritmethics and concept of capacity we conclude that the bottle containing 2 1/2 cups of apple juice contains 5 servings containing 1/2 cups each.
How to determine the quantity of servings from a bottle
In this question we are dealing with capacities, capacities are an application of volumes. A bottle contains a capacity equivalent to a given quantity of cups. The number of cups is found by dividing the capacity of a bottle by the capacity of a serving:
[tex]x = \frac{\frac{5}{2}\,cups}{\frac{1}{2}\,cups }[/tex]
x = 5
By applying aritmethics and concept of capacity we conclude that the bottle containing 2 1/2 cups of apple juice contains 5 servings containing 1/2 cups each.
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Ron runs a hot question ( need answer)
Answers
Answer:
The price of a hot dog decreases between the third and sixth month:
True
The price of a hot dog increases between the sixth and ninth month:
False
The price of a hot dog increases constantly between the ninth and twelfth month:
True
Hope this helps! If anything is wrong, feel free to comment down below so I can change my answer for future users!
john saves N$250 the first month and every two month later increases it by N$75.how much will john save in the 12th month?
Answers
Answer:
750
Step-by-step explanation
HELP PLEASE For the following right triangle, find the side length x.
Answers
Answer:
37
Step-by-step explanation:
use Pytago ( you can search it online )
Determine the exact value of sin 30° tan 45° + tan 30° sin 60⁰
Answers
Answer:
1.
Step-by-step explanation:
1) if sin30=0.5; tan45=1; tan30=1/√3; sin60=√3/2, then
2) 0.5+0.5=1.
Hello everyone!!
This is easy;
[tex] \frac{5x}{2} + \frac{9}{5} = 25[/tex]
Answers
[tex] \frac{5x}{2} + \frac{9}{5} = 25 \\ \frac{25x + 18}{10} = 25 \\ 25x + 18 = 250 \\ \frac{250 - 18}{25} = x \\ x = \frac{232}{25} [/tex]
hope it helps
Please refer to the attachment
Solve the system of equations 3x - 2y = 8 x-2y = 4
Answers
Answer: (2, -1), or x = 2 and y = -1
By graphing:
We can solve by graphing. See attached.
-> The solution is the point of intersection. The lines intersect at (2, -1) which means x is equal to 2 and y is equal to -1.
By substituting:
We can solve this by substituting. It means we will substitute one equation into the other, then solve for the variables.
3x - 2y = 8
x - 2y = 4 -> x = 2y + 4
-
3x - 2y = 8
3(2y + 4) - 2y = 8
6y + 12 - 2y = 8
4y = -4
y = -1
-
x - 2y = 4
x - 2(-1) = 4
x + 2 = 4
x = 2
A record store has 3,108 records evenly shared among 6 rows. How many records are in each row?
Answers
Answer:
518
i don't know if this needs much explaining.
Answer:
518 records per row
Step-by-step explanation:
Divide to find out how many are in each row :
No. of records / No. of rows3,108 / 6518 records per rowWhich is not a reason an athlete uses technology to assess performance?
A. To tailor to their training program.
B. To monitor development.
C. To send to college recruiters.
D. To analyze technique.
Answers
Answer:
C.) To send to college recruiters
Step-by-step explanation:
The correct answer is C.) because this answer choice has nothing to do with assessing an athlete's performance. All of the other options involve assessing performance in some manner. An athelete's performance is directly tied to their training program, development, and technique.
The first aircraft has 59 more seats than the second aircraft. The third aircraft has 42 fewer seats than the second aircraft. If their total number of seats is 407, find the number of seats for each air craft.
Answers
Answer:
first aircraft=189
second aircraft=130
third aircraft=88
Step-by-step explanation:
1st = x+59
2nd = x
3rd= x-42
x + 59 + x + x - 42 = 407
3x + 59- 42 = 407
3x + 17 = 407
3x = 407 - 17
x=390÷3
=130
1st=130+59=189
2nd=130
3rd=130-42=88
Help!, Help! Brainliest Available to Best Answer!
Just find x
Answers
Answer:
x = 50°
Step-by-step explanation:
Let's make 2 equations based on the properties of the triangles :
Applying Exterior Angle Property :
x + 2∠1 = 2√2 (taking ΔABC in perspective)∠1 + 25 = √2 (taking ΔBDC in perspective)Divide equation 1 by 2 :
⇒ 1/2 (x + 2∠1) = 1/2 x (2∠2)
⇒ x/2 + ∠1 = ∠2
⇒ ∠2 - ∠1 = x/2
Similarly, rewrite equation 2 :
⇒ ∠1 + 25 = ∠2
⇒ ∠2 - ∠1 = 25
From these 2 equations, we get :
⇒ x/2 = 25
⇒ x = 25 × 2
⇒ x = 50°
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's consider the figure with two triangles,
Angle b is divided into two equal parts :
let's name each of them as y ~and similarly
Exterior angle C is divided into two equal parts :
let's name each of them z ~Now, according to exterior Angle property :
In Triangle ABC
[tex]\qquad \sf \dashrightarrow \:2y + x = 2z \: \: \: \: [/tex]
[tex]\qquad \sf \dashrightarrow \: 2z - 2y = x \: \: \: \: [/tex]
[tex]\qquad \sf \dashrightarrow \:2(z - y) = x[/tex]
[tex]\qquad \sf \dashrightarrow \:z - y = \dfrac{x}{2} \: \: \: \: \: \: \: - (1)[/tex]
and in Triangle BDC
[tex]\qquad \sf \dashrightarrow \:y + 25 = z \: \: \: \: \: \: \: [/tex]
[tex]\qquad \sf \dashrightarrow \:z - y = 25 \: \: \: \: \: \: \: - (2)[/tex]
equate equation (1) and (2) :
[tex]\qquad \sf \dashrightarrow \: \dfrac{x}{2} = 25[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}{} = 25 \times 2[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}{} = 50 \degree[/tex]