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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.)

Respuesta :

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

[tex]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[/tex]

Hence, our required probability is 0.167.

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