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.
