Question

In a package of 8 expired batteries, three are dead. You chose 2 batteries at random.

What is the expected number of good batteries you get?

Answer 1

The expected number of good batteries you get when choosing 2 batteries at random is 1.43.

Step-by-step explanation:

To find the expected number of good batteries you get when choosing 2 batteries at random from a package of 8 expired batteries, we need to calculate the probability of getting 0, 1, or 2 good batteries.

Out of the 8 expired batteries, 3 are dead, so there are 8 - 3 = 5 good batteries.

The probability of getting 0 good batteries is (3/8) * (2/7) = 6/56.

The probability of getting 1 good battery is (5/8) * (3/7) + (3/8) * (5/7) = 30/56.

The probability of getting 2 good batteries is (5/8) * (4/7) = 20/56.

Therefore, the expected number of good batteries you get is -

(0 * (6/56)) + (1 * (30/56)) + (2 * (20/56)) = 80/56

= 1.43 (approximately).

Answer 2

The expected number of good batteries from choosing 2 batteries at random from a package of 8 expired batteries, where 3 are dead, is approximately 1.2.

Step-by-step explanation:

To find the expected number of good batteries, we need to calculate the probability of getting a good battery for each possible outcome.

Out of the 8 expired batteries, 3 are dead, so there are 5 good batteries.

The probability of getting a good battery on the first draw is 5/8, since there are 5 good batteries out of 8 total.

Similarly, the probability of getting a good battery on the second draw is 4/7, since there will be 4 good batteries left out of 7 total.

To find the expected value, we multiply the probability of each outcome by the number of good batteries in that outcome, and then sum up the results.

Expected number of good batteries = (5/8) * 1 + (4/7) * 1

= 0.625 + 0.571

≈ 1.196