Question

Two dice are thrown at the same time and the product of numbers appearing on them is noted find the probability that the product is a multiple of 3

Answer 1

The observations are :

{ (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1,(2,2),(2,3),(2,4),(2,5),(2,6)

,(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

,(4,1)(4,2)(4,3),(4,4),(4,5),(4,6)

,(5,1),(5,2),(5,3) ,(5,4),(5,5),(5,6)

,(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

We know that ..

P( for getting product is multiple of 3 ) =

$\frac{Number \:of\:favourable\: outcomes}{Total\: number \:of \:outcomes }$

Product of multiple of 3 are :

(1,3),(2,3),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,3),(5,3),(6,3)

When two dice are thrown together the number of possibls outcomes are 36.

We have total number of outcomes = 6 × 6 = 36

And

Number of favourable outcomes = 11

So ..

P = $\dfrac{11}{36}$

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