Question

If A and B are mutually exclusive events of a random experiment and P(not A)=0.45
P(AUB) = 0.65 then find P(B)

P(B)=P(AUB)-P(A)
P(B)=0.65-0.45
=0.20​

Answer 1

Answer:

The value of P (B) is 0.10.

Step-by-step explanation:

If events A and B are mutually exclusive then the joint probability of A and B is 0, i.e. P (A ∩ B) = 0.

Given:

P (not A) = 0.45

P (A ∪ B) = 0.65

Compute the value of P (A) as follows:

$P(A)=1-P(not\ A)\\=1-0.45\\=0.55$

Compute the value of P (B) as follows:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\0.65=0.55+P(B)-0\\P(B)=0.65-0.55\\=0.10$

Thus, the value of P (B) is 0.10.

Answer 2

Answer:

Step-by-step explanation

Since A&B r mutually exclusive A intersection B is '0'.

Therefore, P(A U B) = p(A)+ p(B)

Putting the values from question

.65- .45= p(B)

.20=p(B)