# Find the probability that battery is bad or working

Problem #1 description:

## Find the probability that two purchased batteries will be working.

The probability of buying a bad(faulty) battery in the store is 0.06.
Find the probability that two purchased batteries will be working (not faulty).

Problem #1 solution:
The probability of buying one working battery is equal to:
1 - 0.06 = 0.94

Therefore, the probability of buying two working batteries is:
0.94 × 0.94 = 0.8836

Answer: probability of buying two working batteries is 0.8836

Problem #2 description

## Find the probability that a randomly selected battery will be rejected

The probability that a battery is faulty is 0.02.
The battery quality control system rejects a faulty battery with a probability of P = 0.99, and a working one with a probability of P = 0.01.
Find the probability that a randomly selected battery will be rejected.

Problem #2 solution:
The probability that a randomly selected battery is working equals to 1 - 0.02 = 0.98
Consequently, the probability of rejecting a working battery will be equal to 0.98 × 0.01 = 0.0098
Similarly, the probability of rejecting a faulty battery is 0.02 × 0.99 = 0.0198
Then the probability of rejecting a randomly selected battery will be:
0.0098 + 0.0198 = 0.0296

Answer: probability that a randomly selected battery will be rejected is 0.0296

Next probability problem solution: Find the probability that details are located in no more than 3 boxes

Thursday, July 25, 2024
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