Question

Given that the events A and B are such that P(A)=1/2 , P(A

Answer 1

Answer:

(I) Given events A and B are mutually exclusive

=>P(AUB) = P(A) + P(B)

=>3/5 = 1/2 + p

=>p = 3/5 - 1/2 = 1/10

(II) A and B are independent

=>P(AΠB) = P(A)•P(B) = 1/2 p

=>P(AUB) = P(A) + P(B) - P(AΠB)

=>3/5 = 1/2 + p - 1/2 p

=>3/5 - 1/2 = 1/2 p

=>1/10 = 1/2 p

=>1/5=p

Step-by-step explanation:

Answer 2

Answer:

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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

$Simplify \\ the \\ expression, \\ we \\ get$

(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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