Question

Given that the events A and B are such that P(A) = 1/2, P (A ∪ B) = 3/5, and P(B) = p. Find p if they are

(i) mutually exclusive

(ii) independent

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Answer 1

Answer:

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Step-by-step explanation:

(i) mutually exclusive

P (A ∪ B) = P (A) + P (B) - P (A × B)

$\frac{3}{5} = \frac{1}{2} + \: p - \frac{1}{2} \times p$

$\frac{3}{5} - \frac{1}{2} = p - \frac{1}{2}p$

$\binom{6 - 5}{10} = \binom{2p - p}{2}$

$\frac{1}{10} = \frac{p}{2}$

$p = \frac{2}{10}$

$p = \frac{1}{5}$

(ii) independent

P (A ∪ B) = P (A) + P (B)

$\frac{3}{5} = \frac{1}{2} + p$

$\frac{3}{5} - \frac{1}{2} = p$

$\frac{6 - 5}{10} = p$

$p = \frac{1}{10}$

Answer 2

Step-by-step explanation:

33.Given P(A) =

3

5 and P(B) =

1

5

. Find P(A or B), if A and B are mutually exclusive events.