Two dice are thrown at a time. find the probability that the sum of the outcomes will be 6. a)5/36 b)8/36 c) 4/9 d) 1/3

Options

A. `5//36`
B. `8//36`
C. `4//9`
D. `1//3`

Answer

C

Explanation

`f'(x) = 3x^(2) + 2ax + b`
y = f(x) is increasing
implies `f'(x) ge 0, AA x` and for f'(x) = 0 should not form an interval
`implies (2a)^(2) - 4 xx 3 xx b le 0 implies a^(2) - 3b le 0`
This is true for exactly 16 ordered pairs (a, b), `1 le a, b le 6`, namely (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), and (4, 6) Thus, the required probability is `16//36 = 4//9`