Question

Two dices are thrown. Find the probability that the sum of the digits coming up is divisible by 3 or 4, while the first dice is odd.​

Answer 1

Answer:

Possible sums which are divisible by 3 are 3, 6, 9, 12.

Possible sums which are divisible by 4 are 4, 8, 12.

Let  X  be the sum of two dice output divisible by  3  or  4  

Let  D1  be the output of first dice.

Let  D2  be the output of second dice.

So,  P(X=3)=P(D1=1,D2=2)+P(D1=2,D2=1)  

=136+136  

=236  

P(X=4)=P(D1=1,D2=3)+P(D1=2,D2=2)+P(D1=3,D2=1)  

=336  

P(X=6)=P(D1=1,D2=5)+P(D1=2,D2=4)+P(D1=3,D2=3)+P(D1=4,D2=2)+P(D1=5,D2=1)  

=536  

P(X=8)=P(D1=2,D2=6)+P(D1=3,D2=5)+P(D1=4,D2=4)+P(D1=5,D2=3)+P(D1=6,D2=2)  

=536  

P(X=9)=P(D1=3,D2=6)+P(D1=4,D2=5)+P(D1=5,D2=4)+P(D1=6,D2=3)  

=436  

P(X=12)=P(D1=6,D2=6)  

=136  

P  ( the sum of two dice output divisible by  3  or  4  )   =P(X=3)+P(X=4)+P(X=6)+P(X=8)+P(X=9)+P(X=12)  

=236+336+536+536+436+136  

=2036