Sita and Gita both have a pair of tetrahedral dice who faces are marked as 1,2,3, and 4, The lowest face being regarded as the out come. They throw their dice simultaneously. If P=ab be the probability expressed in lowest term, that the sum of the numbers on their dice is different, find the sum of the digits of value a+b

P=1−Probability that they have equal throw=1−116×116+216×216+316×316+416×416+316×316+216×216+116×116=1−28+161618=1−441616=1−1164P=5364a+b=53+64=117

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Sita and Gita both have a pair of tetrahedral dice who faces are marked as 1,2,3, and 4, The lowest face being regarded as the out come. They throw their dice simultaneously. If $P = \frac{a}{b}$ be the probability expressed in lowest term, that the sum of the numbers on their dice is different, find the sum of the digits of value $(a + b)$

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answer is 117.

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Detailed Solution

$P = 1 - (\Pr o b a b i l i t y t h a t t h e y h a v e e q u a l t h r o w)$

$= 1 - [(\frac{1}{16} \times \frac{1}{16}) + (\frac{2}{16} \times \frac{2}{16}) + (\frac{3}{16} \times \frac{3}{16}) + (\frac{4}{16} \times \frac{4}{16}) + (\frac{3}{16} \times \frac{3}{16}) + (\frac{2}{16} \times \frac{2}{16}) + (\frac{1}{16} \times \frac{1}{16})]$ $= 1 - \frac{28 + 16}{16 (18)} = 1 - \frac{44}{(16) (16)} = 1 - \frac{11}{64}$