Suppose 5 dice are rolled a What is the probabilty that none

Suppose 5 dice are rolled.

a) What is the probabilty that none of the dice come up a mulitple of 3?

b) What is the probability that at least one of the dice comes up a multiple of 3?

Solution

(a)

A dice can come up with nos. 1,2,3,4,5,6

Out of these 6 possibilities only 2 are multiples of 3 (i.e. 3 and 6)

4 possibilities are not multiples of 3

Thus probability that one dice does not come up with a multiple of 3

= 4/6 = 2/3

Since there are 5 dice,

The probability that none of the dice come up a multiple of 3

= (2/3)⁵ = 32/243 =0.131

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(b) Clearly, the probability that at least one of the dice comes up a multiple of 3 =

= 1- The probability that at least one of the dice comes up a multiple of 3

= 1- 32/243

= 211/243 = 0.868