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Suppose you just received a shipment of fourteen televisions. Two of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work.

The probability that both televisions work is ___

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Answer: The probability that both televisions work is approximately 0.746, or 74.6%.

Explanation:

To calculate the probability that both televisions work, we need to find the probability of selecting a working television, and then multiply that by the probability of selecting another working television from the remaining televisions.

Since 2 out of the 14 televisions are defective, that means there are 12 working televisions out of 14. So the probability of selecting a working television on the first draw is 12/14.

After the first television is selected, there will be 13 televisions left, with 11 working televisions. So the probability of selecting a second working television is 11/13.

Therefore, the probability that both televisions work is:

(12/14) x (11/13) = 0.746

So the probability that both televisions work is approximately 0.746, or 74.6%.

To calculate the probability that at least one of the two televisions does not work, we can use the complement rule. The complement of the event "both televisions work" is the event "at least one television does not work."

So, the probability that at least one television does not work is:

1 - 0.746 = 0.254

So the probability that at least one television does not work is approximately 0.254, or 25.4%.

User Scott Hernandez
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