# Problem 420

Suppose  you just  received a shipment of ten television. Five 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 television does not work?

Solution

The general multiplication rule states that the probability that two events E and F both occur is the probability of event E occurring times the probability of event F occurring, given the occurrence of E.

P(E and F ) = P(E)* P(F│E)

Using the general multiplication rule, P(both work) can be found as follows.

P(both work) = P(first works) * P(second works │ first works)

The probability that the first television works is the number of working televisions, 5 divided by r the total number of television, 10

P(first works) = After picking a television that works, there are 9 television remaining and 5 of them are defective. The probability that the next randomly chosen television works is the number of working television, 4, divided by the number of remaining television, 9.

P(second works │ first works) = Then use the general multiplication rule to find the probability that both randomly chosen televisions work, rounding to three decimal places.

P(both work) = P(first works) * P(second works │ first works)

= = 0.222

The probability that at least one of the televisions does not work be found by using a complement. The complement of  P(at least one does not work) is P(both work).

Therefore, use the value found for P(both work) to calculate the probability

P(at least one does not work), rounding to three decimal places.

P(at least one does not work) = 1 – P(both work)

= 1 – 0.222

= 0.778