Statistics Module 2

Find the sample space for the following situation:

You have an urn containing 1 white ball, 4 black balls, and 3 red balls. You randomly pull out two balls at the same time from the urn and record the colors. What is the sample space?

• {W,B,R}

• {W, B, B, B, B, R, R, R}

• {WW, WB, WR, BB, BR, RR}

• {WB, WR, BB, BR, RR}

• {0, 1, 2, 3, 4, 5, 6, 7, 8}

• {1/8, 4/8, 3/8}

• {WB, WR, BB, BR, RR}

Find the sample space for the following situation:

You roll two 4-sided dice, and record the largest of the two numbers. What is the sample space?

• {3, 4}

• {2, 3, 4, 5, 6, 7, 8}

• {1, 2, 3, 4}

• {1/4, 1/4, 1/4, 1/4}

• {11,22,33,44}

{1, 2, 3, 4}

Find the sample space for the following situation:

You roll two 6-sided dice 10 times, and record the number of times the sum is 7. What is the sample space?

• {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

• {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

• {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

• {2, 3, 4, 5, 6, 7}

• {1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36}

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Find the sample space for the following situation:

You flip 3 fair coins, recording the number of heads flipped.

• {0, 3}

• {0, 1, 2, 3}

• {1, 2, 3}

• {H,T}

• {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

{0, 1, 2, 3}

An urn contains 3 Red balls, 10 Green balls, 11 Yellow balls. If you randomly draw one ball, what is the probability it is Yellow?

Round your answer to 4 decimal places.

0.4583

Let X represent the sum of two fair, six-sided die.  Calculate the following:

P(X ≥ 9 and X is even)?

Write your answer as a decimal rounded to 4 decimal places. 

0.1111

An urn contains 3 Red balls, 8 Green balls, 14 Yellow balls. If you randomly draw one ball, what is the probability it is not Yellow?

Round your answer to 4 decimal places.

0.44

Consider a standard deck of 52 cards. What is the probability of a card being Black given it is a Queen?

Round your answer to 4 decimal places.

0.5

A box contains 5 blue blocks, 7 yellow blocks, 15 blue spheres, and 12 yellow spheres. What is the probability you draw a sphere given it is blue?

Round your answer to 4 decimal places.

0.75

Suppose events A and B are independent with P(A) = 0.219 and P(B) = 0.621. Find P(A and B).

Round your answer to 4 decimal places.

0.136

Suppose events A and B are mutually exclusive with P(A) = 0.284 and P(B) = 0.413. Find P(A or B).

Round your answer to 4 decimal places.

0.697

Suppose events A and B are independent with P(A) = 0.272 and P(B) = 0.519. Find P(A^c).

Round your answer to 4 decimal places.

0.728

Suppose events A and B are independent with P(A) = 0.122 and P(B) = 0.652. Find P((A and B)^c).

Round your answer to 4 decimal places.

0.9205

Suppose events A and B are mutually exclusive with P(A) = 0.415 and P(B) = 0.251. Find P((A or B)^c).

Round your answer to 4 decimal places.

0.334

You set up a colorful candy bag for your friend with 3 Cherry, 8 Orange, 5 Lemon, 1 Grape, and 10 Sour Raspberry, hard candies. When they pull out two of them, one for each of you, what is the probability they draw 1 Cherry and 1 Orange in either order?

0.0684

Consider a sample of 120 Nintendo and 112 PlayStation game systems. If 16 Nintendo and 15 PlayStation game systems are defective and one is randomly selected from the sample, find the probability that the game system is Nintendo or defective?

• 0.5819

• 0.1336

• 0.5862

• 0.0323

0.5819

Consider a standard deck of 52 cards. Suppose you draw 5 cards without replacement. What is the probability that the last two cards are Aces, given that the first three are not Aces?

Round your answer to 4 decimal places.

0.0051

Event A and Event B are mutually exclusive. If P(A) = 0.208 and P(B) = 0.674, calculate P(A and B)?

0

What is the probability that someone prefers Cosmos?

Round your answer to 4 decimal places.

0.617

What is the probability that someone is a Faculty member and prefers Dominos?

Round your answer to 4 decimal places.

0.1228

What is the probability that someone prefers Dominos given they are a Student?

Round your answer to 4 decimal places.

0.2218

What is the probability that someone is a Faculty member given they prefer Blackjack? 

Round your answer to 4 decimal places.

0.4688

What is the probability that someone is Student or prefers Blackjack? 

Round your answer to 4 decimal places.

0.7953

Suppose events A and B are mutually exclusive with P(A) = 0.542 and P(A or B) = 0.657. Find P(B).

Round your answer to 4 decimal places.

0.115

Suppose events A and B are independent with P(A) = 0.296 and P(A or B) = 0.568. Find P(B).

Round your answer to 4 decimal places.

0.3864

Suppose events A and B are events with P(A) = 0.29, P(B) = 0.324, and P(A or B) = 0.451. Find P(A and B).

Round your answer to 4 decimal places.

0.163

Find the sample space for the following situation:

You have an urn containing 3 white balls, 6 black balls, and 4 red balls. You randomly pull a ball from the urn and record the color. What is the sample space?

• {1/13, 1/13, 1/13, 1/13, 1/13, 1/13, 1/13, 1/13, 1/13, 1/13, 1/13, 1/13, 1/13}

• {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13}

• {W,B,R}

• {3/13, 6/13, 4/13}

• {W, W, W, B, B, B, B, B, B, R, R, R, R}

{W,B,R}

A pack of Pokemon cards contains 5 fire type, 10 poison type, and 12 water type cards. If you randomly draw one card what the probability it is a water type?

Round your answer to 4 decimal places.

0.4444

Let X represent the sum of two fair, six-sided die.  Calculate the following:

P(X ≥ 6 and X is odd)?

Round your answer to 4 decimal places.

0.3333

Suppose A and B are events with P(A) = 0.546, P(B) = 0.164, and P(A and B) = 0.127. Find P((A or B)^c).

Round your answer to 4 decimal places.

0.417

A bag of mystery jewels contain 19 genuine rubies, 20 imitation rubies, 11 genuine sapphires, and 14 imitation sapphires. What is the probability you draw an imitation stone given it is a ruby?

Round your answer to 4 decimal places.

0.5128

Suppose events A and B are independent with P(A) = 0.171 and P(B) = 0.505. Find P(A and B).

Round your answer to 4 decimal places.

0.0864

You have a bag containing 9 green balls, 15 red balls, and 4 purple balls.  If you draw out three balls, one at a time and without replacement, what is the probability that the third ball is green given that the first two are red?

Round your answer to 4 decimal places.

0.3462

You set up a colorful candy bag for your friend with 8 Cherry, 5 Orange, 12 Lemon, 10 Grape, and 8 Sour Raspberry, hard candies. When they pull out two of them, one for each of you, what is the probability they are both Cherry?

Round your answer to 4 decimal places.

0.031

Considering the information below, what is the probability that someone is a Student and prefers Blackjack? Report your answer rounded to four decimal places.

0.338

Considering the information below, what is the probability that someone is a Faculty member or prefers Blackjack? Report your answer rounded to four decimal places.

0.6531

Considering the information below, what is the probability that someone is a Faculty member given they prefer Cosmos? Report your answer rounded to four decimal places.

0.3125

24 Ravenclaw, 23 Slytherin, 16 Hufflepuff, and 10 Gryffindor students are the only ones to enter their names in the tri-wizard tournament. If only one name is drawn, what is the probability it is not a Ravenclaw student?

Round your answer to 4 decimal places.

0.6712

Consider a sample of 118 Xbox and 125 Atari game systems. If 22 Xbox and 49 Atari game systems are defective and one is randomly selected from the sample, find the probability that the game system is Xbox or defective?

Round your answer to 4 decimal places.

0.6872

Suppose events A and B are mutually exclusive with P(A) = 0.46 and P(A or B) = 0.83. Find P(B).

Report your answer as a decimal rounded to two decimal places.

0.37

Event A and Event B are mutually exclusive. If P(A) = 0.078 and P(B) = 0.23, calculate P((A and B)^c)? 

Round your answer to 4 decimal places.

1