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Question

Two dices are rolled one after the other. The probability that the number on the first is smaller than the number on the second is

A
12
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B
718
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C
34
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D
512
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Solution

The correct option is D 512
Consider the two events as follows:
Ai: getting number i on first die
Bi: getting a number more than i on second die
The recquired probability is
P(A1B1)+P(A2B2)+P(A3B3)P(A4B4)+P(A5B5)=5i=1P(AiBi)=5i=1P(Ai)P(Bi)
[Ai,Bi are independent events]
=16[P(B1)+P(B2)++P(B5)]
=16(56+46+36+26+16)=512

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