Question

Out of a group of 120 students, 28 said they ski and 52 said they snowboard. Sixteen of thestudents said they do both. If a student is chosen at random, find the probability that theysnowboard given they ski (Hint: Draw a Venn Diagram).

Answer 1

Given:

The total number of students = 128 students.

The number of students who play ski, N(S)= 28 students.

The number of students who play snowboard, N(B)= 52 students.

The number of students who play both ski and snowboard, N(S and B)= 16 students.

`N(S\cap B)=16`

Required:

We need to find the probability that they snowboard given they ski.

Step-by-step explanation:

The ven diagram.

Consider the Conditional probability formula.

`P((S)/(B))=(N(S\cap B))/(N(B))`
`Substitue\text{ }N(S\cap B)=16\text{ and N\lparen B\rparen=52 in the formula.}`

`P((S)/(B))=(16)/(52)`
`P((S)/(B))=(4)/(13)`

Final answer:

The probability that they snowboard given they ski is 4/13.