Question

Events E and F are given to be independent . if it is given that P(E)=0.4 and P(E U F) =0.55, then P(F)=?​

Answer 1

Answer:

Given that E and F are to be independent

Then p( E n F ) = 0

And we know that

P( E U F ) = P( E ) + P( F ) + P( E n F )

Then

P( F ) = P( E U F ) – P( E ) – P ( E n F )

P( F ) = 0.55 – 0.4 – 0

P( F ) = 0.15 ans

Answer 2

The value of P(F) = 0.25

Given :

• Events E and F are given to be independent

• P(E) = 0.4 and P(E ∪ F) = 0.55

To find :

The value of P(F)

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that events E and F are independent

So we have P(E ∩ F) = P(E) × P(F)

Also we have P(E) = 0.4 and P(E ∪ F) = 0.55

Step 2 of 2 :

Find the value of P(F)

P(E ∪ F) = 0.55

⇒ P(E) + P(F) - P(E ∩ F) = 0.55

⇒ P(E) + P(F) - P(E) × P(F) = 0.55

⇒ 0.4 + P(F) - 0.4 × P(F) = 0.55

⇒ P(F) - 0.4 × P(F) = 0.15

⇒ 0.6 × P(F) = 0.15

⇒ P(F) = 0.25

Hence value of P(F) = 0.25

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