Question

Out of a group of 120 students that were surveyed about winter sports 28 said they ski 53 said they snowboard Sixteen of the students who said they ski said the also snowboard. If a student is chosen at random P ( snowboard I ski)​

Answer 1

P ( snowboard I ski)​ = 0.5714

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Ski

Event B: Snowboard.

28 out of 120 students ski:

This means that
`P(A) = (28)/(120) = 0.2333`

16 out of 120 do both:

This means that
`P(A \cap B) = (16)/(120) = 0.1333`

P ( snowboard I ski)​

`P(B|A) = (P(A \cap B))/(P(A)) = (0.1333)/(0.2333) = 0.5714`

So

P ( snowboard I ski)​ = 0.5714