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42 votes
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).

Out of a group of 120 students, 28 said they ski and 52 said they snowboard. Sixteen-example-1
User Morten Zilmer
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1 Answer

14 votes
14 votes

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.

Out of a group of 120 students, 28 said they ski and 52 said they snowboard. Sixteen-example-1
User JeffThompson
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3.1k points