Question

Let A and B be two events such that
P(A) = 1/5 While P(A or B) = 1/2
Let P(B) = P. For what values of P
are A and B independent?​

Answer 1

P(A) = 1/5. P(B) = p

P(A or B) = 1/2

P(A or B) = p(A)•p(B).

[Since A and B are independent]

1/2=1/5•p

P = 5/2

Answer 2

The value of P = 0.375

Given :

A and B be two events such that P(A) = 1/5 While P(A or B) = 1/2 , P(B) = P.

To find :

The value of P such that A and B independent

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that ,

A and B be two events such that P(A) = 1/5

Now P(A) = 1/5 = 0.2

P(A or B) = 1/2 = 0.5

P(B) = P.

Step 2 of 2 :

Find the value of P

It is given that A and B independent

∴ P(A ∩ B) = P(A).P(B)

Now we have ,

P(A or B) = 0.5

⇒ P(A ∪ B) = 0.5

⇒ P(A) + P(B) - P(A ∩ B) = 0.5

⇒ 0.2 + P(B) - P(A).P(B) = 0.5

⇒ 0.2 + P - 0.2 × P = 0.5

⇒ P - 0.2P = 0.5 - 0.2

⇒ 0.8P = 0.3

⇒ P = 0.3/0.8

⇒ P = 0.375

Hence the required value of P = 0.375

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