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But the answer should be 11/138.

11/138? Give me second.

This solution does indeed give you \[11 \over 138\]

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

What are you using as the addition rule?

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

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)?

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

Oh I see! Thanks!

you're welcome.