A die is thrown. If E is the event ‘the number appearing is a multiple of 3’ and F be the event ‘the number appearing is even’ then find whether E and F are independent?

Solution

S = {1, 2, 3, 4, 5, 6}
E = {3, 6}, F = {2, 4, 6}, $straight E intersection straight F space equals space open curly brackets 6 close curly brackets$
$therefore space space space straight P left parenthesis straight E right parenthesis equals space space 2 over 6 space equals 1 third comma space space space straight P left parenthesis straight F right parenthesis space equals 3 over 6 space equals space 1 half comma space space straight P left parenthesis straight E space intersection space straight F right parenthesis space equals space 1 over 6$
Since P(E and F) = $1 over 6 space equals 1 third cross times 1 half space equals space straight P left parenthesis straight E right parenthesis space cross times space straight P left parenthesis straight F right parenthesis$
∴ the events E and F are independent events.

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Probability

A die is thrown. If E is the event ‘the number appearing is a multiple of 3’ and F be the event ‘the number appearing is even’ then find whether E and F are independent?

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