Represent and Determine Probability Question
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Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.8
At Monarch Collegiate Institute, a survey was conducted about the number of students who play rugby and the number of students who read science fiction books. Let R be the event that a student plays rugby, and S be the event that a student reads science fiction books. If there were 60 students surveyed, P(R|S) = 5/7, P(S|R) = 1/3, and P(S) = 7/60, which of the following expressions gives the number of students who said they play rugby and why? Choose all correct answers.
- 60(760⋅5713), by applying the general Multiplication Rule to find P(R), then multiplying by 60.
- 60(1-760+(760⋅57)), since it can assumed that everyone who doesn't read science fiction plays rugby. Therefore, subtract P(S) from one, but add back in P(S and R) (found using the general Multiplication Rule), and then multiply by 60.
- 760⋅13=7180=P(S and R), 60(718057), by applying the general Multiplication Rule to find P(S and R), then using it again to find P(R) and then multiplying by 60.
- Not possible. If 60 is multiplied by 5/7 (the conditional probability of choosing someone who plays rugby, given that they read science fiction), the number is not a whole number. This means that either the total number of participants or this probability is incorrect.