In a simultaneous throw of a pair of dice, find the probability of getting an even number on one and a multiple of 3 on the other
Solution
In a throw of pair of dice, total no of possible outcomes = 36 (6 × 6) 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)
E ⟶ event of getting an even no. on one and a multiple of 3 on other
No. of favorable outcomes = 11 {(2, 3) (2, 6) (4, 3) (4, 6) (6, 3) (6, 6), (3, 2), (3,4
),
(3, 4) , (3, 6) , (6, 2) , (6, 4)}
Total no. of possible outcomes = 36
We know that, Probability P(E) =`"No.of favorable outcomes"/"Total no.of possible outcomes"`
P(E) =11/36
