Question

There are 50 AAA batteries in a box and 5 are defective. Two batteries are selected without replacement. What is the probability of selecting a defective battery followed by another defective battery?

Answer 1

2/245 ≈ 0.008163

Explanation:

You want the probability of choosing 2 defective batteries from as box of 50 batteries when 5 in the box are defective. Selection is done without replacement.

Choices

There are 5C2 ways that 2 defective batteries can be chosen. There are 50C2 ways that 2 batteries can be chosen. The desired probability is ...

p(2 defective) = 5C2/50C2 = 2/245 ≈ 0.008163

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Additional comment

nCk = n!/(k!(n-k)!)

The probability of interest is the product of the probabilities of a bad battery on the first choice and a bad battery on the second choice:

(5/50)(4/49) = 4/490 = 2/245

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