Question

A and B will take the same 10-question examination. Each question will be answered correctly by A with probability .7, independently of her results on other questions. Each question will be answered correctly by B with probability .4, independently both of her results on the other questions and on the performance of A. (a) Find the expected number of questions that are answered correctly by both A and B. (b) Find the variance of the number of questions that are answered correctly by either A or B.

Answer 1

Answer:

a) The expected number of questions that are answered correctly by both A and B = 11 (7 + 4).

b) The Variance of the number of questions that are answered correctly by either A or B = 2.25.

Step-by-step explanation:

Number of questions in the examination = 10

Probability of A's answer being correct = 0.7

Probability of B's answer being correct = 0.4

The expected number of questions that are answered correctly by both A and B:

           Probability of       Expected        

        Correct Answer       Value          Variance

A              0.7                     7 (0.7 * 10)    2.25

B              0.4                     4 (0.4 * 10)    2.25

Total expected value =    11

           Mean =                  5.5                2.25