If E1 and E2 are mutually exclusice events, then

Engineering

Mathematics

Conditional Probability

Question

If E₁ and E₂ are mutually exclusice events, then

$P(E 1) + P(E 2) \leq 1$

$P(E 1) + P(E 2) \geq 1$

$P(E 1) + P(E 2) = 1$

$None of these$

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Two events are mutually exclusive if they donot occur at the same time
Given E₁ and E₂ are mutually exclusive events. Venn diagram is given by

In case of mutually exclusive events

P(E₁∩E₂) = 0

P(E₁UE₂) = P(E₁) + P(E₂) – P(E₁∩E₂)

P(E₁UE₂) = P(E₁) + P(E₂)

Case (i): mutually exclusive and exhaustive

P(E₁UE₂) = 1

P(E₁) + P(E₂) = 1 ... (1)

Case (ii): mutually exclusive but not exhaustive (0 ≤ P(E₁UE₂) ≤ 1)

P(E₁UE₂) > P(E₁) + P(E₂) ... (2)

from (1) and (2)

P(E₁) + P(E₂) ≤ 1

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