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Leokris [45]
3 years ago
10

A new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries wil

l be independently selected and tested until two acceptable ones have been found. Suppose that 90% of all batteries have acceptable voltages.What is the probability that you test exactly 4 batteries
Mathematics
1 answer:
klio [65]3 years ago
3 0

Answer:

The probability that you test exactly 4 batteries is 0.0243.

Step-by-step explanation:

We are given that a new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found.

Suppose that 90% of all batteries have acceptable voltages.

Let the probability that batteries have acceptable voltages = P(A) = 0.90

So, the probability that batteries have unacceptable voltages = P(U) = 1 - P(A) = 1 - 0.90 = 0.10

Now, the probability that you test exactly 4 batteries is given by the three cases. Firstly, note that batteries will be tested until two acceptable ones have been found.

So, the cases are = P(AUUA) + P(UAUA) + P(UUAA)

This means that we have tested 4 batteries until we get two acceptable batteries.

So, required probability = (0.90 \times 0.10 \times 0.10 \times 0.90) + (0.10 \times 0.90 \times 0.10 \times 0.90) + (0.10 \times 0.10 \times 0.90 \times 0.90)

     =  0.0081 + 0.0081 + 0.0081 = <u>0.0243</u>

<u></u>

Hence, the probability that you test exactly 4 batteries is 0.0243.

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