Question

Two dice are thrown simultaneously find the probability of getting



a.Multiple of.2 on one dice and multiple of 3 on other.Dice

Answer 1

case 1- when dice 1 is getting a multiple of two and dice 2 is getting multiple of 3. so in this case , combination will be-
p(a)= (2,3) , (2,6), (4,3) , (4,6) , (6,3) , (6,6) = Six way
case 2- when dice 2 is getting a multiple of two and dice 1 is getting multiple of 3. so in this case , combination will be-
p(b) = (3,2) , (6,2) , (3,4) , (6,4) , (3,6), (6,6) = Six way
p(a∩b) = (6,6) = 1 way
total no of chances= p(a)+p(b)-p(a∩b) = 11
total operation = 6*6 = 36
hence probability = 11/36

Answer 2

Total outcomes=36

Let E= Event of getting a multiple of 2 on one dice and a multiple of 3 in another dice.

Here the multiple of 2 are 2,4,6 and multiple of 3 are 3,6 .

So favourabl outcomes for E are (2,3) (4,3) (6,3) (2,6) (4,6) (6,6) (3,2) (3,4) (3,6) (6,2),(6,4)

~ number of outcomes favourable to E =11

Therefore

required probability =p(E)

=11/36

so. and is 11/36