Question

Event A has probability 0.5. Event B has probability 0.6. Which of the following must be true?

a. A and B are disjoint.
b. A and B must include all possible outcomes in the sample space.
c. The probability that A does not occur is 0.5.
d. All of the above.

Answer 1

Answer: c. The probability that A does not occur is 0.5.

Explanation:

Given: Event A has probability 0.5. Event B has probability 0.6.

If M and N are disjoint sets , the P(M or N) = P(M) +P(N)

So, if A and B are disjoint sets , then P(A or B)= P(A) + P(B)

= 0.5+0.6

= 1.1 > 1

And probability cannot be greater than 1.

So, A and B are not disjoint.

If A or B includes all the possible outcomes in the sample space then, P(A) or P(B) should equal to 1 which is not true.

Probability of not E = 1- P(E)

So, . The probability that A does not occur = 1- P(A) = 1-.5= 0.5

So, option is C. correct.

The probability that A does not occur is 0.5.