Probability

Concept:
For any two events

A

and

B

, the probability of their union is given by:

P(A%20%5Ccup%20B)%20%3D%20P(A)%20%2B%20P(B)%20-%20P(A%20%5Ccap%20B)

A

and

B

are independent events, then:

P(A%20%5Ccap%20B)%20%3D%20P(A)P(B)

Thus, the formula becomes:

P(A%20%5Ccup%20B)%20%3D%20P(A)%20%2B%20P(B)%20-%20P(A)P(B)

Step 1: Find

P(A%20%5Ccap%20B)

using independence.

P(A%20%5Ccap%20B)%20%3D%20P(A)P(B)

Substitute the given values:

P(A%20%5Ccap%20B)%20%3D%200.4%20%5Ctimes%200.5%20%3D%200.20

Step 2: Apply the union formula.

P(A%20%5Ccup%20B)%20%3D%20P(A)%20%2B%20P(B)%20-%20P(A%20%5Ccap%20B)

Substitute the values:

P(A%20%5Ccup%20B)%20%3D%200.4%20%2B%200.5%20-%200.20

P(A%20%5Ccup%20B)%20%3D%200.70

%5Ctherefore%20P(A%20%5Ccup%20B)%20%3D%200.70

Chapter Questions
1 MCQs