Question

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability? of obtaining the same number on both dice?

Answer 1

Total no. of possible outcomes when 2 dice are thrown = 6 × 6 = 36 which 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)

Let E ⟶ event of obtaining the same no. on both dice

No. of favourable outcomes = 6 {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}

P(E) =`"No.of favorable outcomes"/"Total no.of possible outcomes"`

P(E) =6/36 =1/6