If 5% of all light bulbs a company manufactures are defective, the probability of any one bulb being defective is 0.05. What is the probability that four bulbs drawn independently from the company's stock will be defective? Round your answer to eight decimal places.
A)0.06250000
B)0.00000031
C)0.00012500
D)0.00000625
E)0.00000000

Question

If 5% of all light bulbs a company manufactures are defective, the probability of any one bulb being defective is 0.05. What is the probability that four bulbs drawn independently from the company's stock will be defective? Round your answer to eight decimal places. ​
A)0.06250000
B)0.00000031
C)0.00012500
D)0.00000625
E)0.00000000

Quizplus · Accepted Answer

To find the probability of all four bulbs being defective, we can use the multiplication rule of probability for independent events. The probability of the first bulb being defective is 0.05, the probability of the second bulb being defective given that the first bulb is already defective is also 0.05, and so on for the third and fourth bulbs. Therefore, the probability of all four bulbs being defective is:
0.05 x 0.05 x 0.05 x 0.05 = 0.00000625
Rounding this to eight decimal places gives us the answer of 0.00000625, which corresponds to choice D.

If 5% of All Light Bulbs a Company Manufactures Are