Math CentralQuandaries & Queries


Question from Carol, a student:

Suppose 3 of 12 bottles in a case of wine are bad. If you randomly select 2 bottles what is the probability that one is good and one is bad

Hi Carol,

To save myself some typing I am going to let A be the event that you choose one good bottle and one bad bottle. Then

= P([choose good then bad] or [choose bad then good])
= P(choose good then bad) + P(choose bad then good)

Why is there not a third term there?

The probability that you choose a good bottle on your first choice is 9/12. If you chose a good bottle then there are 11 bottles left, 3 of which are bad so the probability you choose a bad bottle at this point is 3/11. Thus

P(choose good then bad) = 9/12 times 3/11

Can you finish the problem now?

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