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

1.	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
Answer» Given: E₁ and E₂are 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(E₁∩ E₂) = 0 Hence, P(E₁∪ 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 E₁and E₂ are independent.

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

Answer»

Given: E₁ and E₂are 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(E₁∩ E₂) = 0

Hence, P(E₁∪ 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 E₁and E₂ are independent.

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