Question

(ii) Given that the events A and B are such that :
P (A) =3/5. P(AUB) = 1/2 and P (B) = p.
Find the value of 'p' if the events are independent.​

Answer 1

Step-by-step explanation:

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Given, P(A) = 1/2 ,

P (A ∪ B) = 3/5

and P(B) = p.

For Mutually Exclusive

Given that, the sets A and B are mutually exclusive.

Thus, they do not have any common elements

Therefore, P(A ∩ B) = 0

We know that P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

Substitute the formulas in the above-given formula, we get

3/5 = (1/2) + p – 0

$Simplify \\ the \\ expression, \\ we \\ get</p><p>$

(3/5) – (1/2) = p

(6 − 5)/10 = p

1/10 = p

Therefore, p = 1/10

Hence, the value of p is 1/10, if they are mutually exclusive.

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