Chapter 5

Question 1

what letter represents a probability set?

Answer 1

S

Question 2

what is the law of large numbers?

Answer 2

when an experiment is performed many, many times, the relative frequency of an event tends to become closer to the actual probability

Question 3

what is the union of two events?

Answer 3

the set of elements in either A or B
the probability that A, B, or both will occur

Question 4

what is the union of two events denoted as?

Answer 4

AUB

Question 5

what is the intersection of two events?

Answer 5

the set of elements in both A and B
the probability that both events will occur

Question 6

what is the intersection of two events denoted as?

Answer 6

A∩B

Question 7

what is a complement to an event?

Answer 7

the probability of the event not occurring

Question 8

how can you find the complement to an event?

Answer 8

1 - the probability

Question 9

what is the complement to an event denoted as?

Answer 9

P(A’) or P(A^c)

Question 10

what is an “and” probability?

Answer 10

an intersection probability

Question 11

how do you calculate an “and” probability?

Answer 11

P(A) x P(B) = P(A∩B)
P(A|B) x P(B) = P(A∩B)

Question 12

what is an “or” probability?

Answer 12

a union probability

Question 13

how do you calculate an “or” probability?

Answer 13

P(A) + P(B) - P(A∩B) = P(AUB)

Question 14

t/f: for mutually exclusive events, P(A∩B) = 0 (explain why if this is false)

Answer 14

true (the two events cannot occur simultaneously, therefore there is no intersection)

Question 15

what are independent events?

Answer 15

events where knowing that one event occurs does not change the probability of the other one occurring

example: flipping a coin

Question 16

how do you test for independence?

Answer 16

P(A|B) = P(A)
this shows that B had no effect

P(B|A) = P(B)
this shows that A had no effect

P(A∩B) = P(A) x P(B)

Question 17

what are conditional events?

Answer 17

the probability of one event occurring given that the other event occurs

Question 18

how do you find the probability of a conditional event?

Answer 18

P(A|B) = P(A∩B) / P(B)

Question 19

t/f: disjointed is not another way to say mutually exclusive

Answer 19

false: it is another way to say mutually exclusive

Question 20

what are mutually exclusive events?

Answer 20

events that have no outcomes in common and can never occur simultaneously

example: flipping both heads and tails at the same time

Question 21

what are the first branches of a tree diagram called?

Answer 21

unconditional probabilities

Question 22

what are the second branches of a tree diagram called?

Answer 22

conditional probabilities

Question 23

what are the third branches of a tree diagram called?

Answer 23

joint probabilities

Question 24

t/f: the joint probabilities of a tree diagram must add up to 1

Answer 24

true

Question 25

how do you find a joint probability?

Answer 25

multiply the unconditional and conditional probabilities

Question 26

if you had a tree diagram about gender and owning/not owning a dog, how would you find the probability of owning a dog?

Answer 26

add the joint probabilities of owning a dog

Question 27

how are “given” probabilities calculated using a tree diagram?

Answer 27

usually, it is a joint probability divided by an unconditional probability, but this can be reversed

Question 28

how should you start with venn diagrams?

Answer 28

if possible, fill in the middle/intersection part (the “and” probability) first