Question

Let A and B be two independent events. If p(A)=3/5 and p(B')=1/3 then the value of p(AUB)' is equal to?

Answer 1

Answer:

P(AUB)'=2/15

Step-by-step explanation:

According to the Question,

• Given That, A and B be two independent events. If P(A)=3/5 and P(B')=1/3.

So, P(B)=1-P(B') ⇒ P(B)=1-(1/3) ⇔ P(B)=2/3

• The Product Rule of Probability says For independent events P(A∩B)=P(A)×P(B)

P(A∩B)=3/5 × 2/3 ⇒ P(A∩B)=2/5

• We know, P(AUB)=P(A)+P(B)-P(A∩B)

Thus, P(AUB)= 3/5 + 2/3 - 2/5

P(AUB)=1/5 + 2/3

P(AUB)=(3+10)/15 ⇔P(AUB)=13/15

• Now, The Value Of P(AUB)'=1-P(AUB) ⇔ 1 - 13/15 ⇒ P(AUB)'=2/15