A survey of a class of 32
students found that 17
students are girls, 11
students participate in clubs, and 10
students both are girls and participate in clubs.
What is the probability that a student participates in clubs, given that the student is a girl?
Responses
1032
10 over 32
1710
17 tenths
1117
11 over 17
10/17
The probability that a student participates in clubs, given that the student is a girl, is 10/17.
A leather store performs an observational survey of women walking through a mall. There were 30
women that walked by in an hour. Of those women, 18
were carrying purses, 12
were wearing belts, and 6
were both carrying purses and wearing belts.
What is the probability that a woman was wearing a belt, given that the woman was also carrying a purse?
Responses
2/5
2 fifths
1/3
1 third
1/2
1 half
1/5
The probability that a woman was wearing a belt, given that the woman was also carrying a purse, is 1/3 or 1 third.
Given the following probabilities, for what P(B)
are events A
and B
independent?
P(A)=12
P(A and B)=16
Responses
1/4
1 fourth
3/4
3 fourths
1/3
1 third
1/8
Events A and B are independent if and only if P(A and B) = P(A) * P(B).
Given that P(A) = 1/2 and P(A and B) = 1/6, let's find the value of P(B):
P(A and B) = P(A) * P(B)
1/6 = 1/2 * P(B)
1/6 = P(B)/2
1/6 * 2 = P(B)
1/3 = P(B)
So the value of P(B) that makes events A and B independent is 1/3 or 1 third.
An experiment consists of rolling a standard six-sided die once. Event A
is "rolling an even number" and event B
is "rolling a 2.{}^{\prime\prime}
Are the events dependent or independent? Why?
Select the option that correctly answers both questions.
Responses
Events A
and B
are dependent, because P(B)≠P(B|A).
Events cap A and cap b are dependent, because P(B)≠P(B|A).
Events A
and B
are independent, because P(A)=P(B|A)=12.
Events cap A and cap b are independent, because
Events A
and B
are independent, because P(B)=P(B|A)=16.
Events cap A and cap b are independent, because
Events A
and B
are dependent, because P(A)≠P(B|A).