A shipment of portable radios contains 14 good radios and 3 defective ones. If two are randomly selected (without replacement) and tested, find the probability that at least one will be defective.

Check 180 baskets out of 18000 for defects 3 are defective how many should he predict are defective?

A shipment of 10 TV's contains 3 defective sets. How many ways can a hospital purchase 4 of these sets and receive at least 2 defective sets?

15

To find the probability that at least one of the two radios selected will be defective, we can use the concept of complementary probability.

The complementary probability is the probability of the opposite event occurring. In this case, the opposite event is that both radios are good (i.e., none of them are defective).

To calculate the probability that both radios are good, we need to consider the number of good radios and the total number of radios left after each selection.

First, let's find the probability of selecting a good radio for the first selection. We have 14 good radios out of a total of 17 radios (14 good + 3 defective), so the probability of selecting a good radio is 14/17.

After the first selection, we have 16 radios left (since one was already selected), out of which 13 are good and 3 are defective. Thus, the probability of selecting a good radio for the second selection is 13/16.

To find the probability of both radios being good, we multiply the probabilities of each selection since the events are independent:

P(both radios are good) = (14/17) * (13/16) = 182/272.

Now, we can find the probability of at least one defective radio using the complementary probability:

P(at least one defective) = 1 - P(both radios are good) = 1 - (182/272) = 90/272.

The probability that at least one radio will be defective is 90/272.