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Example 11 - Let event A be 'odd number on first throw' - Examples

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  1. Class 12
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Example 11 An unbiased die is thrown twice. Let the event A be ‘odd number on the first throw’ and B the event ‘odd number on the second throw’. Check the independence of the events A and B. Two events A & B are independent if P(A ∩ B) = P(A) . P(B) An unbiased die is thrown twice S = Let us define two events as A : odd number on the first throw B : odd number on the second throw A ∩ B = odd number on the first & second throw = { (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)} So, P(A ∩ B) = 9﷮36﷯ = 1﷮4﷯ Now, P(A) . P(B) = 1﷮2﷯ × 1﷮2﷯ = 1﷮4﷯ Since P(A ∩ B) = P(A) . P(B), Therefore, A and B are independent events

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