Question

A pair of fair dice is thrown. Find the probability that the sum is 10 or greater if 5 appears on the first die.

Solution

Let the events be
E : sum is 10 or greater
F : 5 appears on the first die.
$therefore space space space space space space space space straight E space equals space open curly brackets left parenthesis 4 comma space 6 right parenthesis comma space space left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 5 comma space 6 right parenthesis comma space left parenthesis 6 comma space 4 right parenthesis comma space left parenthesis 6 comma space 5 right parenthesis comma space left parenthesis 6 comma space 6 right parenthesis close curly brackets space space space space space space$
$straight F space equals space open curly brackets left parenthesis 5 comma space 1 right parenthesis comma space left parenthesis 5 comma space 2 right parenthesis comma space left parenthesis 5 comma space 3 right parenthesis comma space left parenthesis 5 comma space 4 right parenthesis comma space left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 5 comma space 6 right parenthesis close curly brackets$
$straight E intersection straight F space equals space open curly brackets left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 5 comma space 6 right parenthesis close curly brackets$
$therefore space space space space space straight P left parenthesis straight E right parenthesis space equals space 6 over 36 comma space space space straight P left parenthesis straight F right parenthesis space equals 6 over 36 comma space space straight P left parenthesis straight E intersection straight F right parenthesis space equals 2 over 36$
Required probability = $fraction numerator straight P left parenthesis straight E intersection straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction space equals 2 over 6 space equals 1 third.$

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Probability

A pair of fair dice is thrown. Find the probability that the sum is 10 or greater if 5 appears on the first die.

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