Question

Find the indicated probability. A bin contains 72 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary. (Hint: sampling with replacement = independent events)

Answer 1

Answer:

The answer to the nearest thousandth is 0.473

Step-by-step explanation:

Number of light bulbs = 72

Number of defective light bulbs = 10

Number of good light bulbs = 72 - 10 = 62

Probability of selecting a defective light bulb =  P(defective) = 10/72

The probability of selecting a good light bulb = P(good) = 62/72

5 number of light bulbs are selected with replacement and all being good is given by

P(all bulbs are good) = $(\frac{62}{72} )$×$(\frac{62}{72} )$×$(\frac{62}{72} )$×$(\frac{62}{72} )$×$(\frac{62}{72} )$ = 0.473473

The answer to the nearest thousandth is

0.473