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Let E1 and E2 be the events such that P(E1) = 1/3 and P(E2) = 3/5.

Find:

(i) P(E1∪ E2), when E1 and E2 are mutually exclusive.

(ii) P(E1∩ E2), when E1 and E2 are independent

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Given: E1 and E2 are two events such that P(E1) = \(\frac{1}{3}\) and P(E2) = \(\frac{3}{5}\)

To Find: 

(i) P(E1 ∪ E2) when E1 and E2 are mutually exclusive.

We know that,

When two events are mutually exclusive P(E∩ E2) = 0

Hence, P(E∪ E2) = P(E1) + P(E2)

\(\frac{1}{3}+\frac{3}{5}\)

\(\frac{14}{15}\)

Therefore , P(E1 ∪ E2) = \(\frac{14}{15}\) when E1 and E2 are mutually exclusive.

(ii) P(E1 ∩ E2) when E1 and E2 are independent.

We know that when E1 and E2 are independent ,

P(E1 ∩ E2) = P(E1) x P(E2)

\(\frac{1}{3}\times \frac{3}{5}\)

\(\frac{1}{5}\)

Therefore, P(E1 ∩ E2) = \(\frac{1}{5}\) when E1 and E2 are independent.

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