Given a sample space, and events A and B, where P (A) = 0.5 and P (B) = 0.5. Which of the following values for P (A and B) are not possible?

a. All are possible

b. 0.35

c. 0.5

d. 0

e. 0.25

Option a, option b, option c, option d are not possible values for P (A ∩ B)

Solution:

Given A and B are independent events.

P (A) = 0.5 and P (B) = 0.5

To find which of the following values for P (A and B) are not possible.

P (A and B) = P (A ∩ B)

P (A ∩ B) = P (A) * P (B)

= 0.5 * 0.5

P (A ∩ B) = 0.25

Option a: All are possible.

All answers are not possible for two independent events.

Option b: 0.35

We found that P (A and B) is 0.25.

So, 0.35 is not possible value.

Option c: 0.5

We found that P (A and B) is 0.25.

So, 0.5 is not possible value.

Option d: 0

We found that P (A and B) is 0.25.

So, 0 is not possible value.

Option e: 0.25

We found that P (A and B) is 0.25.

So, 0.25 is the possible value.

Hence, 0.35, 0.5, 0 are not possible values.