First slide
Theorems of probability
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

Moderate
Solution

Consider two events as follows: 

Ai: getting number i on first die 

Bi: getting a number more than i on second die .

The required probability is 

PA1B1+PA2B2+PA3B3+PA4B4 +PA5B5=i=15PAiBi=i=15PAiPBiAi,Bi are independent] =16PB1+PB2++PB5=1656+46+36+26+16=512

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