Question

When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 12?
A) 35/36
B) 17/36
C) 15/36
D) 1/36

Answer 1

The total number of possibilities is 6 for the first die and 6 for the second. Since each throw on the first die could be paired with any of the six on the second, the total ways the dice could fall is 6 × 6 = 36.

The probability of getting 12 or more =1/36

So the probability of getting less than 12 = 1 -1/36

=35/36

Answer 2

$\underline{\underline{\Huge\mathfrak{Answer ;}}}$

=> When two dice are thrown simultaneously, the probability is n(S)= 6x6 = 36

=> Required, the sum of the two numbers that turn up is less than 12

=> That can be done as n(E)

=> { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5) }

= 35

• Hence, required probability = n(E)/n(S) = 35/36.

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@dmohit432