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There are two die A and B both having si...

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

Text Solution

Verified by Experts

The correct Answer is:
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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