Question

A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have acceptable voltages. Suppose that 90% of all batteries from a certain supplier have acceptable voltages. Among fifteen randomly selected flashlights, what is the probability that at least fourteen will work? (Round your answer to three decimal places.)

Answer 1

0.549 or 54.9%

Explanation:

This is a binomial distribution (Bernoulli's experiment), where the probability of “success” (selecting a battery with acceptable voltage) is 0.9 and the probability of “failure” is 0.1

So, the probability of selecting at least 14 acceptable batteries out of 15 is

`\large C(15,14)(0.9)^(14)(0.1) + C(15,15)(0.9)^(15)`

where C(n, m) are combinations of n elements taken m at a time.

C(15,14) = 15

C(15,15) = 1

so, the probability we are looking for is

`\large 15*(0.9)^(14)0.1+(0.9)^(15)=0.3431+0.2058 = 0.549 = 54.9\%`