Data Management (MDM4U) · Probability Distributions

Conditional probability

Compute conditional probability P(A | B) from a two-way survey summary. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MDM4U-PD2.1

Try one

A survey of 40 grade 12 students found that 21 play a school sport. Of those, 20 have a part-time job. Of the remaining 19 who don't play a school sport, 6 have a part-time job. If you randomly pick one of the students who play a school sport, what is the probability that they don't have a part-time job?

Answer: 1/21

See one solved, step by step

A survey of 60 students found that 27 take the school bus. Of those, 24 live more than 3 km from school. Of the remaining 33 who don't take the school bus, 21 live more than 3 km from school. If you randomly pick one of the students who take the school bus, what is the probability that they live more than 3 km from school?

📘 Worked solution
1Only consider the students who take the school bus -- there are 27 of them.Conditional probability restricts the sample space to the group you're told about.
2P(lives far | takes the bus) = 2427 = 89Of those 27 students, 24 also live more than 3 km from school.

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