Question

If the probability that event A occurs is0.51,the probability that event B occurs is 0.64 and that probability that both A and B occur is 0.23 then:

1. events A and B are complementary

2. events A and B are mutually exclusive

3. events A and B are not mutually exclusive

4. events A and B are statistically independent

Answer #1

We check all options wheter they hold truth.

1)

A and B are complementary if A^{c} = B

That is

( 1 - P(A) ) = P(B)

1 - 0.51 = 0.49 0.64

A and B are complemetary- **FALSE**

2)

Events A and B are mutually exclusive if P(Aand B) = 0

Since P(A and B) = 0.23 0

Therefore, A and B are mutually exclusive -
**FALSE**

3)

A and B are not mutually exclusive - **True**

4)

A and B are indipendent if P(A and B) = P(A)* P(B)

Since P(A) * P(B) = 0.51 * 0.64 = 0.3264 P(A and B)

Therefore,

Events A and B are independent - **False**

Option 3 is correct

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