Question

Two dice one blue and one red are thrown at the same time. Write down all the possible outcomes. (2)

i) What is the probability that the sum of the two numbers appearing on the top of the dice is 8. (1)

ii) Product of the number on the top of the dice is12. (1)

iii) The number on first die is a factor of number on the second die​

Answer 1

All possible outcomes:-

(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)

i) $P(E) = \frac{No. of favorable outcomes}{Total no. of outcomes}$

       Total no. of outcomes = 36

        No. of fav. outcomes = (2,6) (3,5) (4,4) (5,3) (6,2) = 5

        ∴ $P(E) = \frac{5}{36}$

ii) No. of fav. outcomes = (2,6) (3,4) (4,3) (6,2)  = 4

     ∴ $P(E) = \frac{4}{36} = \frac{1}{9}$

iii) No. of fav. outcomes = (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,2) (2,4) (2,6) (3,3) (3,6)                            

                                           (4,4) (5,5) (6,6) = 14

   ∴$P(E) = \frac{14}{36} = \frac{7}{18}$