KVPY SX SB Exam 19-Nov-2017 Question Paper

Question : 10 of 120

Marks: +1, -0

A pair of 12-sided fair dice with faces numbered 1,2,3, ....., 12 is rolled. The probability that the sum of the numbers appearing has remainder 2 when divided by 9 is

$7/72$
$5/48$
$11/144$
$1/9$

Validate

Solution:

x_1 + x_2 = 11 \or \ x_1 + x_2 = 20

x_1 + x_2 = 11

possible cases
(1,10)
(2,9)
(3,8)
(4,7)
(5,6)
or

x_1 + x_2 = 20

(8,12)
(9,11)
(10,10)

10/144+6/144=16/144=1/9

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