Question

a barrel of 20 apples has 2 rotten apples and 18 good apples. 7 apples are seleected at random frm the barrel. what is the expected number of good apples sellected

Answer 1

To calculate the expected number of good apples out of 7 randomly selected from a barrel containing 18 good and 2 rotten apples, multiply the number of selections (7) by the proportion of good apples in the barrel (18/20), resulting in an expectation of 6.3 good apples.

Step-by-step explanation:

The student is asking how to find the expected number of good apples selected when 7 apples are chosen at random from a barrel that contains 18 good apples and 2 rotten apples. The expected value can be found by using the following formula:

Expected value (E[X]) = n × (k/N)

• n is the number of apples selected (7 in this case).
• k is the number of good apples in the barrel (18 in this case).
• N is the total number of apples in the barrel (20 in this case).

Using the formula, the expected number of good apples (E[X]) selected would be:

E[X] = 7 × (18/20)

E[X] = 7 × 0.9

E[X] = 6.3

We can expect to have, on average, 6.3 good apples selected from the barrel.