adnanchowdhury 3 years ago In a lottery there are 24 prizes allocated at random to 24 prize-winners. Ann, Ben, and Cal are three of the winners. Of the prizes, 4 are cars, 8 are bicycles and 12 are watches. Find the probability that Ann gets a car and Ben gets a car or bicycle

1. KingGeorge

${4 \over 24} \times {20 \over 24}$The 4/24 is Ann's chance of getting a car, and the 20/24 is Ben's chance of getting a car or a bike.

But the answer should be 11/138.

3. KingGeorge

11/138? Give me second.

4. KingGeorge

My bad, I was calculating the probability that Ben got a bike or a watch, not a bike or a car. In this case, the probability is given by ${4 \over 24} \times {{3+8} \over 23}$Where 4/24 is the probability that Ann gets a car, and the other term is the chance Ben got a car plus the chance he got a bike.

5. KingGeorge

This solution does indeed give you $11 \over 138$

Thanks a lot! Can you work out ben's probability using the addition rule?

7. KingGeorge

What are you using as the addition rule?

For ben: P(Car) + P(Bicycle) - P(Bicycle and car)

9. KingGeorge

nm, I realized I knew it. By the addition rule, Ben's probability is P(Car)=$$3 \over 23$$ and P(Bike) =$$8 \over 23$$ so P(Car)+P(Bike)=P(Car or Bike)=$${3 \over 23}+{8 \over 23}={11 \over 23}$$

10. KingGeorge

This works because Ben only gets one prize. If he were to get more than one prize, this wouldn't work.

The addition rule is: P(A U B) = P(A) + P(B) - P(A and B).

So how come you don't need to subtract P(A and B)?

13. KingGeorge

In this case P(A and B)=0 since he can only get one prize.

Oh I see! Thanks!

15. KingGeorge

you're welcome.