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.

Explanation:

The ven diagram.

Consider the Conditional probability formula.

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

$P(\frac{S}{B})=\frac{16}{52}$$P(\frac{S}{B})=\frac{4}{13}$

Final answer:

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