Determine the following probabilities. Enter your final answers as reduced fractions. Two coins are flipped. Find the probability that the first coin land on heads and the second coin lands on heads. Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is black and the second card is a 8. A single digit between 0 and 9 is randomly chosen, and a single letter from A to Z is randomly chosen. Find the probability that the number is 4 and the letter is a consonant. Two dice are rolled. Find the probability that first die lands on an even number and the second die is less than 2.

Answers

Answer 1

The probability of an event occurring is given by the ratio of the number of

possible outcome to the number of required outcome.

First question: The probability that the first coin lands on heads and the second coin lands on tails is 0.25.Second question: The probability of drawing a black card and then a 8 is [tex]\underline{\dfrac{1}{13}}[/tex].

Third question: The probability that the number chosen is 4 and the letter chosen is a consonant, is [tex]\underline{\dfrac{21}{234}}[/tex].

Fourth question: The probability that the first die lands on an even number and the second die is less than 2, is [tex]\underline{\dfrac{1}{12}}[/tex].

Reasons:

First question:

The number of faces in a coin = 2; A head or a tail

The probability that the first coin lands on heads, P(H) = [tex]\dfrac{1}{2}[/tex]

The probability that the second coin lands on tails, P(T) = [tex]\dfrac{1}{2}[/tex]

The probability that the first coin lands on heads and the second coin lands

on tails = P(H ∩ T)

Which gives;

[tex]P(H \cap T) = \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}[/tex]

The probability that the first coin lands on heads and the second coin lands on tails = [tex]\dfrac{1}{4}[/tex] = 0.25

Second question:

The number of black cards in a pack of 52 = 26 cards

The number of cards that are a 8 in a pack of 52 cards = 8 cards

[tex]\mathrm{The \ probability \ of \ drawing \ a \ black \ card}, \ P(B) = \dfrac{26}{52} = \dfrac{1}{2}[/tex]

[tex]\mathrm{The \ probability \ of \ drawing \ a \ 8,} \ P(8) = \dfrac{8}{52} = \dfrac{2}{13}[/tex]

The probability of drawing a black card and then an 8, P(B∩8), is given as follows;

[tex]P(B \cap 8) = \dfrac{1}{2} \times \dfrac{2}{13} = \dfrac{1}{13}[/tex]

The probability of drawing a black card and then a 8 is P(B∩8) = [tex]\underline{\dfrac{1}{13}}[/tex]

Third question:

The probability that a number chosen between 0 and 9 is 4, P(4) = [tex]\dfrac{1}{9}[/tex]

The number of consonant in the alphabet = 21

The probability that a letter chosen from A to Z is a consonant, P(C) = [tex]\dfrac{21}{26}[/tex]

The probability that the number chosen is 4 and the letter chosen is a consonant, P(4 ∩ C)  = [tex]\dfrac{1}{9} \times \dfrac{21}{26} = \underline{ \dfrac{21}{234}}[/tex]

Fourth question:

The number of even numbers on a die = 3; (2, 4, 6)

The number of numbers less than 2 on a die = 1

The probability that the first die lands on an even number, P(E) = [tex]\dfrac{3}{6}[/tex]

The probability that the second die is less than 2. P(<2) = [tex]\dfrac{1}{6}[/tex]

Therefore;

The probability that the first die lands on an even number and the second die is less than 2, P(E ∩ <2) = [tex]\dfrac{3}{6} \times \dfrac{1}{6} = \dfrac{3}{36} = \underline{\dfrac{1}{12}}[/tex]

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Related Questions

plz, tell me the answer. and plz explain if you can

Answers

Answer:

angel b is 70 because all the degrees in a triangle must add up to 180

Complete the statement with always, sometimes, or never.
The terms of a polynomial are ________ monomials.

Answers

Answer:

always

Step-by-step explanation:

The terms of a polynomial are _always_ monomials.

A polynomial is a sum of monomials.

‘Always’ is the answer

Explain why 4:6 and 8: 10 are not
equivalent ratios.

Answers

Answer:

Because when 4:6 is simplified, you get 2:3, but when 8:10 is simplified, you get 4:5

So, they are not equivalent ratios because their simplified ratios are not the same.

Step-by-step explanation:

Hope this is helpful.

Since the value of the given ratios are different they can not be said to be the equivalent ratio.

What is the ratio?

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

It is given that the two ratios are 4:6 and 8: 10.

Ratios with the same value are said to be equivalent. If we multiply both portions of a ratio by the same number, we can create comparable ratios.

The ratio 4/6 is in the lowest term is 2/3 equal to 0.66

The ratio 8/10 is in the lowest term is 4/5 equal to 0.8

The values of both ratios are different.

Thus, the values of the given ratios are different they can not be said to be the equivalent ratio.

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the tens digit was 1. The ones digit was 6. The number was between 600 and 700 what was the number

Answers

Answer:

616

Step-by-step explanation: hope it helps :)

Answer:665,830 my answer

Step-by-step explanation:

so. what have you got so far?

How can a digit have no value?

The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 14 vans and 6 buses with 564 students. High School B rented and filled 4 vans and 6 buses with 414 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

Answers

Answer:

No of student can be found using x+y=total

X+y=total

Concept

Step-by-step explanation:

Let vans be x

Let bas be y

14x+6y=564

4x+6y=414

With that you can get the answer am sorry I couldn't give the appropriate answer I only showed the way am in a trip that's why

Reina's family is taking a road trip. Their car can travel no more than 304 miles without needing to refill the gas tank. They have traveled 221 miles since they last filled the gas tank. Reina knows that the inequality representing this situation is 221 + x < 304. Select from the drop-down menu to correctly interpret the solution of this inequality. Reina's family can drive ______ more miles before they need to refill the gas tank.​

Answers

Solving the inequality, it is found that the correct interpretation of the solution is:

Reina's family can drive 83 more miles before they need to refill the gas tank.​

The amount x of miles they can still travel is modeled by the following inequality:

[tex]221 + x \leq 304[/tex]

To solve it, we treat it similarly to an equality, hence:

[tex]x \leq 304 - 221[/tex]

[tex]x \leq 83[/tex]

Hence:

Reina's family can drive 83 more miles before they need to refill the gas tank.​

A similar problem is given at https://brainly.com/question/11713066

The answer prior to this is WRONG. The correct answer is "at most 83" miles.

Plz help fast I will mark Brainlyist

Answers

Hey, here it is!!
Can u give me a brainliest answer??

m
Hope it helpes!!!

WILL GIVE BRAINLEST!!! A rational expression has been simplified below
(x-2)(x+6) X-2
7(x+6)
*=2
For what values of xare the two expressions equal?

Answers

Answer:

You're answer is B. All answers except -6

Step-by-step explanation:

did the test

Margie's hourly salary is $6. 75. Last week she worked a 20âhour week. How much did she earn?.

Answers

Answer:

125

Step-by-step explanation:

6.25 x 20 = 125

Scored 12 out of 39 in the test work out the percentage

Answers

30.8%

I did 12/39 in my calculator and got .308 then multiplyed by 100 to get 30.8%

At the Lincoln County Animal Shelter, there are currently 6 dogs and 4 cats. Write the ratio of cats to dogs in simplest form as a fraction.

Answers

Answer:

2/3

Step-by-step explanation:

4 cats / 6 dogs  = 2/3

simplify by dividing by 2

4:6

2:3

2/3

Find the GCD (or HCF) of numerator and denominator. GCD of 6 and 4 is 2.

6 ÷ 24 ÷ 2.

Reduced fraction: 32. Therefore, 6/4 simplified to lowest terms is 3/2.

since you’re wanting cats to dogs, just flip it

Which of the following is equal to this expression? (254 * 64) 1/4

Answers

Answer:

4064

Step-by-step explanation:

254*64=16256*1/4=4064

YES I Am GIVING A BRAINLIST pls be accurate
One equation in a system of equations is y = 4x + 5. Which equation below would have to be the second equation so that the system has (1, 9) as its only solution?

Question 5 options:

y = 3x - 1


y = 5x + 4


y = -2x - 8


y = 6x - 8

Answers

Answer:

y = 5x +4

Step-by-step explanation:

x has to equal 1

y = 5(1) +4 = 9

WILL GIVE BRAILIEST, HELP! :(
Land in Wisconsin is for sale to property investors. A 232 acre lot is listed for sale for 200,500, assuming the same price what size lot could you purchase at 100,000?

-120 acres
-182.9 acres
-115.72 acres
-120.71 acres

Answers

Answer:

115.72 acres

Step-by-step explanation:

232/200,500 = 0.001157

100,000*0.001157 = 115.7 acres

The ratio of students in Class X to Class Y is 2 : 5. There are 24 more students in Class Y than Class X. How many students must transfer from Class Y to Class X so that both classes have equal number of students?

Answers

Answer:

The answer will be 12 students. 12 students must transfer from Class Y to Class X so that both classes have equal number of students.

Step-by-step explanation:

Since the ratio is 2 : 5, we would multiply both number to 8 and get 16 : 40.

Now find the average of those two numbers: (16 + 40) / 2 which gets you 28. Now either subtract 16 from 28 or subtract 28 from 40 and you will get 12.

28 - 16 = 12 students

40 - 28 = 12 students.

C=pi/2 what is the area?

Answers

Answer:

A=1

Step-by-step explanation:

The formula to find the area of a circle is πr^2, meaning that you divide the diameter in half which is 1. So 1^1 is one. The area would be one.

Hope this helps :)

The area would be one, is, A=1.

What is area of circle?

The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr2. π is approximately  3.142

here, we have,

C=pi/2

The formula to find the area of a circle is πr^2,

meaning that you divide the diameter in half which is 1.

So 1^1 is one.

The area would be one.

To learn more on area of circle click:

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Domain and rangeeeeeee

Answers

Answer:

domain: -4 ≤ x ≤ 2

range: 2 ≤ y ≤ 6

Step-by-step explanation:

EASY POINTS
2+2=?
4+4=?
6+6=?

Answers

Answer:

Below

Step-by-step explanation:

2+2 = 4

4+4= 8

6+6=12

I will give brainliest who ever answers fastest what is 1+1=?

Answers

Answer:

2

Step-by-step explanation:

Like and give 5 star rating

in the equation f(x) = 5x + 6,6 is called?

Answers

Answer:

the y-intercept

Step-by-step explanation:

Answer: y-intercept

Step-by-step explanation:

Since f(x) = 5x + 6 is in the slope-intercept form (y = mx + c), then that would make 6 the y-intercept.

What is the fractional equivalent of the repeating decimal 04?
O A.
B.
4
100
C
D.
4
99
NEED HELP ASAP‼️‼️

Answers

Let's see

[tex]\\ \rm\rightarrowtail x=0.444\dots[/tex]

[tex]\\ \rm\rightarrowtail 10x=4.44\dots[/tex]

From both

9x=4x=4/9

Is this answer right?

Answers

Answer:

correct.

Step-by-step explanation:

Pharaoh, Diego, and Devonte all got jobs
at different clothing stores. At Pharaoh's
store it costs $48 to get 3 shirts. At Diego's
store it costs $96 to get 16 shirts. At
Devonte's store it costs $56 to get 14
shirts. Which one is the best deal.

Answers

Answer:

i think the answer is Devonte's  store because you get 14 shirt for $56

Step-by-step explanation:

Pharaoh's good it's not too expensive but you only get 3 shirts , Diego's is too expensive even if you get 16 shirts it's for $96

if a car uses one gallon of gas every 25 miles how much miles would he make with 8 gallons

Answers

Step-by-step explanation:

One gallon = 25 miles

8 gallon= 25×8 miles= 200 miles

Kyle read 3 5/6 books and Jan read 2 1/3 books. How many more books did Kyle read than Jan?

Answers

Answer:

3 5/6 = 3 10/12

2 1/3= 2 4/12

3-2=1

10/12-4/12= 6/12=1/2

so Kyle read 1 1/2 more books then Jan

Answer:

Kyle read [tex]1 \frac{1}{2}[/tex] books more than Jan

Step-by-step explanation:

Let's put our equation

[tex]3 \frac{5}{6}-2\frac{1}{3}[/tex]

They have different denominators so let's look for the [tex]LCM[/tex] to find our common denominator

Find our LCM

Definition of LCM - LCM stands for least common multiple. The least common multiple of two numbers is the smallest number that is a multiple of both of them.

Now let's find our LCM

[tex]6:6,12,18,24,30,36,42\\\\3:3,6,9,12,15,18,21,24,27,30[/tex]

as you can see our [tex]LCM[/tex] is [tex]6[/tex]

Now our fraction is[tex]3\frac{5}{6}-2\frac{2}{6}[/tex]Solve

[tex]3\frac{5}{6}-2\frac{2}{6}=1 \frac{3}{6}[/tex] this can be reduced to [tex]1 \frac{1}{2}[/tex]

Kyle read [tex]1 \frac{1}{2}[/tex] books more than Jan

Brainliest please :)

What is a logarithm.

Answers

Answer:

Logarithms were invented in the 17th century as a calculation tool by Scottish mathematician John Napier (1550 to 1617), who coined the term from the Greek words for ratio (logos) and number (arithmos

Step-by-step explanation:

Peter says if you subtract 16 from my number and multiply the difference by negative 5 the result is negative 50 what is peter's number?

Answers

Answer:

Below.

Step-by-step explanation:

If n is the required number:

(n - 16) * -5 = -50

-5n + 80 = -50

-5n = -50 - 80

-5n = -130

n = -130 / -5

n = 26 (answer).

Whats 16 x 32 what does it equal

Answers

512 16 times 32: 512



The first term of an arithmetic sequence is 10. The 7th term is 28. What is the common difference of the arithmetic sequence?

Answers

Answer:

the answer is A1

Step-by-step explanation:

{a7} = 10 = a1 + 7*4

   10 = a1 + 28

  -28         - 28

 -18 = a1

1 + 1 PLEASE HELP AN EXPERT CANT EVEN ANSWER THIS

Answers

ITS 15 100% CORRECT

Answer:

1+1=2!!!!!!!!

YAY HAHAHAHAHAHA

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