Question

You have seven cards, numbered 3 through 9, and you pick one at random. If you pick a card with a prime number, you get 1 point; if you pick a card with a composite number, you lose 1 point. Find the expected value of the number of points you get.

Answer 1

He has
`(-1)/(7)` number of points

Explanation:

We have given that numbers from 3 to 9

So numbers will be 3,4,5,6,7,8,9

Here prime numbers are 3,5,7

And composite numbers are 4,6,8,9

So probability of getting prime number =
`(3)/(7)`

And probability of getting composite number
`=(4)/(7)`

It is given that if he gets prime number then he get 1 point and if he get composite number then he loss 1 point '

So value of number of point he has =
`1* (3)/(7)-1* (4)/(7)=(-1)/(7)`