the probability for event a is 0.4, the probability for event b is 0.2, and the probability of events a and…

the probability for event a is 0.4, the probability for event b is 0.2, and the probability of events a and b is 0.1. why are the events not independent? the sum of p(a) and p(b) is greater than p(a and b). the product of p(a) and p(b) is greater than p(a and b). the product of p(a) and p(b) is not equal to p(a and b). the sum of p(a) and p(b) is not equal to p(a and b).

the probability for event a is 0.4, the probability for event b is 0.2, and the probability of events a and b is 0.1. why are the events not independent? the sum of p(a) and p(b) is greater than p(a and b). the product of p(a) and p(b) is greater than p(a and b). the product of p(a) and p(b) is not equal to p(a and b). the sum of p(a) and p(b) is not equal to p(a and b).

Answer

Explanation:

Step1: Recall independence formula

For two independent events (A) and (B), (P(A\cap B)=P(A)\times P(B)).

Step2: Calculate (P(A)\times P(B))

Given (P(A) = 0.4) and (P(B)=0.2), then (P(A)\times P(B)=0.4\times0.2 = 0.08).

Step3: Compare with (P(A\cap B))

Given (P(A\cap B)=0.1), and (0.08\neq0.1), i.e., (P(A)\times P(B)\neq P(A\cap B)).

Answer:

The product of (P(A)) and (P(B)) is not equal to (P(A) and (B)).