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 80% 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

To find the probability that at least fourteen flashlights will work, we need to consider the probability of exactly fourteen working plus the probability of exactly fifteen working. We can use the binomial distribution to calculate these probabilities.

Step-by-step explanation:

To find the probability that at least fourteen flashlights will work, we need to consider the probability of exactly fourteen working plus the probability of exactly fifteen working. Since each flashlight requires two batteries, we can use the binomial distribution to calculate these probabilities.

The probability of exactly fourteen flashlights working is given by:

P(X = 14) = C(15, 14) * (0.8)14 * (0.2)1

The probability of exactly fifteen flashlights working is given by:

P(X = 15) = C(15, 15) * (0.8)15 * (0.2)0

The probability of at least fourteen flashlights working is the sum of these two probabilities:

P(X ≥ 14) = P(X = 14) + P(X = 15)

Answer 2

Answer: Our required probability is 0.167.

Step-by-step explanation:

Since we have given that

n = 15

Probability of success p = 80% = 0.8

Probability of failure q = 20% = 0.2

We need to find the probability that at least fourteen will work.

So, by Binomial distribution, we get that

`P(X\geq 14)=P(X=14)+P(X=15)\\\\P(X\geq 14)=^(15)C_(14)(0.8)^(14)(0.2)+^(15)C_(15)(0.8)^(15)\\\\P(X\geq 14)=0.167`

Hence, our required probability is 0.167.