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Five Dice Are Thrown Simultaneously. If the Occurrence of an Odd Number in a Single Dice is Considered a Success, Find the Probability of Maximum Three Successes. - Mathematics

Five dice are thrown simultaneously. If the occurrence of an odd number in a single dice is considered a success, find the probability of maximum three successes.

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Solution

Success = `p = 3/6 = 1/2`

Failure = `q = 1/2`

`P(x = r) = ""^nC_r p^r q^(n-r)`

Here n = 5, r = 0,1,2,3

`p =1/2 , q = 1/2`

Maximum three success = `P(0) + P(1) + P(2) + P(3)`

`= ""^5C_0 (1/2)^5 + ""^5C_1 (1/2)^5 + ""^5C_2(1/5)^5 + ""^5C_3 (1/2)^5`

`= (1/2)^5  [1 + 5 + 10 + 10]`

`= 26/32 = 13/16`

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