A fishing rod has 25 guides, 5 of which are defective. If 2 are selected at random with replacement, find the probability that both are defective.
Question
A fishing rod has 25 guides, 5 of which are defective. If 2 are selected at random with replacement, find the probability that both are defective.
Solution
When the problem says "with replacement," it means that after a guide is selected, it is put back into the pool before the next one is selected. This means that the probabilities stay the same for each selection.
The total number of guides is 25, and there are 5 defective ones. So, the probability of selecting a defective guide on any given selection is 5/25 = 0.2.
Since we're selecting 2 guides, and we want to know the probability that both are defective, we multiply the probabilities together.
So, the probability that both guides selected are defective is 0.2 * 0.2 = 0.04.
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