Two different dice are rolled together. Find the probability of getting:
(i) The sum of numbers on two dice to be 5.
(ii) Even numbers on both dice.
Two different dice are rolled together. Find the probability of getting:
(i) The sum of numbers on two dice to be 5.
(ii) Even numbers on both dice.
When two dice are thrown simultaneously, the possible outcomes are
1234561(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)2(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)3(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)4(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)5(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)6(6,1)(6,1)(6,3)(6,4)(6,5)(6,6)
∴ Total number of favouable outcomes = 9
We know
Probablility of an event =Total number of favourable outcomesTotal number of outcomes
(1) The outcomes favourable of the event 'the sum of the numbers on two dice to be 5' denoted by E are (1,4), (2,3), (4,1) and (3,2).
Total number of favourable outcomes = 4
∴PE=436=19
(ii) The outcomes favourable to the event 'even numbers on both dice' denoted by F are (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4) and (6,6).
Total number of favouable outcomes = 9
∴PF=936=14
When two dice are thrown simultaneously, the possible outcomes are
1234561(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)2(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)3(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)4(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)5(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)6(6,1)(6,1)(6,3)(6,4)(6,5)(6,6)
∴ Total number of favouable outcomes = 9
We know
Probablility of an event =Total number of favourable outcomesTotal number of outcomes
(1) The outcomes favourable of the event 'the sum of the numbers on two dice to be 5' denoted by E are (1,4), (2,3), (4,1) and (3,2).
Total number of favourable outcomes = 4
∴PE=436=19
(ii) The outcomes favourable to the event 'even numbers on both dice' denoted by F are (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4) and (6,6).
Total number of favouable outcomes = 9
∴PF=936=14
