Question

in a certain shipment of 13 phones, 8 are defective. 7 of the phones are selected at random without replacement. what is the probability that 5 of the 7 phones are defective? express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

The probability of selecting 5 out of 7 defective phones is approximately 0.3263.

Step-by-step explanation:

To find the probability that 5 out of 7 randomly selected phones are defective, we need to use the concept of hyper-geometric distribution.

The probability of selecting 5 defective phones out of 7 is given by:

P(5 defective phones) = (C(8,5) * C(5,2)) / C(13,7)

where C(n,r) represents the combination of n items taken r at a time.

By evaluating the expression, we find that:

P(5 defective phones) = (56 * 10) / 1716

= 0.3263

Therefore, the probability that 5 of the 7 randomly selected phones are defective is approximately 0.3263, rounded to four decimal places.