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There are two die A and B both having six faces. Die A has three faces marked with 1, two faces marked with 2, and one face marked with 3. Die B has o

Monjur Alahi

There are two die A and B both having six faces. Die A has three faces marked with 1, two faces marked with 2, and one face marked with 3. Die B has one face marked with 1, two faces marked with 2, and three faces marked with 3. Both dices are thrown randomly once. If E be the event of getting sum of the numbers appearing on top faces equal to x and let P(E) be the probability of event E, then P(E) is maximum when x equal to
A. 5
B. 3
C. 4
D. 6


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Salim Ahmed Kawsar

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Correct Answer - C
x can be 2, 3, 4, 5, 6. The number of ways in which sum of 2, 3, 4, 5, 6 can occur is given by the coefficients of `x^(2), x^(3), x^(4), x^(5), x^(6)` in
`(3x + 2x^(2) + x^(3))(x + 2x^(2) + 3x^(3)) = 3x^(2) + 8x^(3)+ 14x^(4) + 8x^(5) + 3x^(6)`
This shows that sum that occurs most often is 4.

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