You have a drawer that has twenty batteries in it and you know that six of them

Question

You have a drawer that has twenty batteries in it and you know that six of them are completely dead. (Why you didn’t throw them away at the time is a mystery, but you didn’t and now you want to throw away the dead ones.) You start picking out batteries one at a time and testing them. You are not putting any batteries back in the drawer until you’ve removed all the dead ones. What is the probability that

The first two you choose are both good.

At least one of the first three works.

The first four you pick will all work.

You have to pick five batteries to find one that works.

Explanation / Answer

Number of good>

Number of dead>

P(first two you choose are both good) = 14C2/20C2 = 0.479

P(at least one of the first three works) = 1 - P(none of first three works)

= 1 - 6C3/20C3

= 1 - 0.018

= 0.982

P(the first four you pick will all work) = 14C4/20C4 = 0.207

P(You have to pick five batteries to find one that works) = P(first 4 didnot work and fifth one works)

= (6C4/20C4) x 14/16

= 0.0027

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