Module 2
Multiplication law of probability
two or more events are independent if the prob. of one does not affect the prob. of the other
Suppose events A and B are mutually exclusive with P(A) = 0.086 and P(B) = 0.062. Find P((A or B)c).
0.852
Event A and Event B are mutually exclusive. If P(A) = 0.295 and P(B) = 0.541, calculate P(A and B)?
0
Consider a standard deck of 52 cards. Suppose you draw 4 cards without replacement. What is the probability that the last two cards are Queens, given that the first two are not Queens?
0.0049
You set up a colorful candy bag for your friend with 6 Cherry, 7 Orange, 12 Lemon, 13 Grape, and 11 Sour Raspberry, hard candies. When they pull out two of them, one for each of you, what is the probability they are both Sour Raspberry? (Round your answer to 4 decimal places.)
0.0468
Suppose events A and B are independent with P(A) = 0.798 and P(B) = 0.144. Find P(A and B). (Round your answer to 4 decimal places.)
0.1149
You set up a colorful candy bag for your friend with 5 Cherry, 6 Orange, 5 Lemon, 2 Grape, and 5 Sour Raspberry, hard candies. When they pull out two of them, one for each of you, what is the probability they draw 1 Orange and 1 Sour Raspberry in either order?
0.1186
Suppose events A and B are events with P(A) = 0.349, P(B) = 0.269, and P(A or B) = 0.467. Find P(A and B).
0.151
Suppose events A and B are independent with P(A) = 0.259 and P(A or B) = 0.42. Find P(B).
0.2173
A pack of Pokemon cards contains 6 fire type, 9 poison type, and 16 water type cards. If you randomly draw one card what the probability it is a poison type? (Round answer 4 decimal places)
0.2903
An urn contains 11 Red balls, 13 Green balls, 12 Yellow balls. If you randomly draw one ball, what is the probability it is Green?
0.3611
Suppose events A and B are independent with P(A) = 0.613 and P(B) = 0.625. Find P(A and B). (Round your answer to 4 decimal places.)
0.3831
Suppose events A and B are independent with P(A) = 0.586 and P(B) = 0.509. Find P(Ac).
0.414
Suppose A and B are events with P(A) = 0.504, P(B) = 0.155, and P(A and B) = 0.103. Find P((A or B)c). (Round your answer to 4 decimal places.)
0.444
A box contains 15 blue blocks, 6 yellow blocks, 12 blue spheres, and 7 yellow spheres. What is the probability you draw a sphere given it is blue?
0.4444
You have a bag containing 13 green balls, 10 red balls, and 6 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.)
0.4815
Consider a standard deck of 52 cards. What is the probability of a card being Black given it is a Queen?
0.5
Suppose events A and B are mutually exclusive with P(A) = 0.18 and P(A or B) = 0.74. Find P(B).
0.56
A bag of mystery jewels contain 9 genuine rubies, 23 imitation rubies, 11 genuine sapphires, and 15 imitation sapphires. What is the probability you draw an imitation stone given it is a sapphire? (Round your answer to 4 decimal places.)
0.5769
Consider a sample of 112 Nintendo and 91 PlayStation game systems. If 21 Nintendo and 11 PlayStation game systems are defective and one is randomly selected from the sample, find the probability that the game system is Nintendo or defective? A.) 0.1576 B.) 0.6552 C.) 0.0313 D.) 0.6059
0.6059
Suppose events A and B are mutually exclusive with P(A) = 0.284 and P(B) = 0.413. Find P(A or B).
0.697
An urn contains 9 Red balls, 7 Green balls, 15 Yellow balls. If you randomly draw one ball, what is the probability it is not Red? (Round your answer to 4 decimal places.)
0.7097
Suppose events A and B are mutually exclusive with P(A) = 0.214 and P(A or B) = 0.935. Find P(B).
0.721
8 Ravenclaw, 8 Slytherin, 13 Hufflepuff, and 21 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 Hufflepuff student? (Round your answer to 4 decimal places.)
0.74
Consider a sample of 72 Nintendo and 138 PlayStation game systems. If 21 Nintendo and 18 PlayStation game systems are defective and one is randomly selected from the sample, find the probability that the game system is Playstation or defective? (Round your answer to 4 decimal places.)
0.7571
Suppose events A and B are independent with P(A) = 0.518 and P(B) = 0.35. Find P((A and B)c).
0.8187
Event A and Event B are mutually exclusive. If P(A) = 0.303 and P(B) = 0.404, calculate P((A and B)c)?
1
sample space
A set listing all the probabilities for an event
Simple event
A single element of the sample space
mutually exclusive
Events that cannot occur at the same time.
mutually exclusive equation
P (A and B) = 0
Dependent Events
P(A and B) = P(A) * P (B/A)
Independent Events
P(A and B) = P(A) x* P(B)
Addition law of probability
P(A or B) = P(A) + P(B) − P(A and B)
Events in the same sample space can add up to be more than 1. A.) True, if they are mutually exclusive. B.) True, if they are not mutually exclusive. C.) False, events in the same sample space can never add up to be more than 1. D.) True, only if they are not independent.
True, if they are not mutually exclusive.
Event
any subset of the sample space
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 a ball out, note the color, and replace it. You do this 6 times, and record the number of times you drew a white ball. What is the sample space? A.) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} B.) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} C.) {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} D.) {2, 3, 4, 5, 6, 7, 8} E.) {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, 11, 12}
Find the sample space for the following situation: You flip 3 fair coins, recording the number of heads flipped. A.) {0, 3} B.) {0, 1, 2, 3} C.) {1, 2, 3} D.) {H,T} E.) {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
{0, 1, 2, 3}
Find the sample space for the following situation: You roll two 6-sided dice, and record their sum. What is the sample space? A.) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} B.) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} C.) {1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36} D.) {2, 3, 4, 5, 6, 7, 8} E.) {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
