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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 7

Lesson 3: Conditional probability

# Conditional probability using two-way tables

Researchers surveyed 100 students on which superpower they would most like to have. This two-way table displays data for the sample of students who responded to the survey:
SuperpowerMaleFemaleTOTAL
Fly261238
Invisibility123244
Other10818
TOTAL4852100
A student will be chosen at random.
problem 1
Find the probability that the student chose to fly as their superpower.
P, left parenthesis, start text, f, l, y, end text, right parenthesis, equals

problem 2
Find the probability that the student was male.
P, left parenthesis, start text, m, a, l, e, end text, right parenthesis, equals

problem 3
Find the probability that the student was male, given the student chose to fly as their superpower.
P, left parenthesis, start text, m, a, l, e, space, end text, vertical bar, start text, space, f, l, y, end text, right parenthesis, equals

problem 4
Find the probability that the student chose to fly, given the student was male.
P, left parenthesis, start text, f, l, y, space, end text, vertical bar, start text, space, m, a, l, e, end text, right parenthesis, equals

problem 5
Is this statement about conditional probability true or false?
"In general, P, left parenthesis, start text, A, space, end text, vertical bar, start text, space, B, end text, right parenthesis, equals, P, left parenthesis, start text, B, space, end text, vertical bar, start text, space, A, end text, right parenthesis. You can reverse the order and the probability is the same either way."