The Product Rule, or the Multiplicative Rule

Question 


Suppose that we have a fuse box containing 20 fuses, of which 5 are defective. If 2 fuses are selected at random and removed from the box in succession without replacing the first, what is the probability that both fuses are defective?


The probability that both fuses are defective is 5/20 x 4/19 = 5/95.

explaination:

The probability that the first fuse is defective is 5/20. The second fuse is dependent on the first, so the probability that the second fuse is also defective is 4/19 (since there are now 4 defective fuses left out of 19 total). The probability of both being defective is the product of the two, which is 5/20 x 4/19 = 5/95.


elaborate the law for the above probability

The law for probability states that the probability of two independent events occurring together is the product of the probabilities of the individual events occurring. In this case, the two events are selecting two fuses from the fuse box. The probability of the first fuse being defective is 5/20 and the probability of the second fuse being defective is 4/19 (since there are now 4 defective fuses left out of 19 total). The probability of both being defective is the product of the two, which is 5/20 x 4/19 = 5/95.

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