**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