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

Answer:

He has $\frac{-1}{7}$ number of points

Step-by-step 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 = $\frac{3}{7}$

And probability of getting composite number $=\frac{4}{7}$

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 = $1\times \frac{3}{7}-1\times \frac{4}{7}=\frac{-1}{7}$