The Vardon Exploration Company is getting ready to leave for South America to explore for oil. One piece of equipment requires 10 batteries that must operate for more than 2 hours. The batteries being used have a 15 percent chance of failing within 2 hours. The exploration leader plans to take 15 batteries. Assuming that the conditions of the binomial apply, the probability that the supply of batteries will not contain enough good ones to operate the equipment is:
A) 0.0449
B) 0.0132
C) 0.9832
D) 0.0168

Question

Quizplus · Accepted Answer

The probability that the supply of batteries will not contain enough good ones to operate the equipment can be calculated using the binomial probability formula. Given that the probability of failure for each battery is 15% (or 0.15), the probability of success (a battery not failing) is 85% (or 0.85). The exploration leader takes 15 batteries but needs at least 10 to not fail. We calculate the probability of 0 to 5 failures (which corresponds to having at least 10 good batteries) and subtract this from 1 to find the probability of not having enough good batteries. The correct answer involves calculating these probabilities and finding the complement, which leads to the answer provided.

The Vardon Exploration Company Is Getting Ready to Leave for South