Question

a pair of dice is rolled . what is the probability that the sum of the numbers is an odd number and a multiple of 3 ?

Answer 1

Answer:

Multiple of 3 can be 3,6,9 and 12

Odd number can be 1,3,5,7,9,11

Therefore, the intersection of two criteria are 3 and 9

∴ Pr(Getting 3 or 9)=2/36=1/18

Hope this helps :)

Step-by-step explanation:

Answer 2

Given,

2 dice are rolled together

To Find,

The probability that the sum of the numbers is an odd number and a multiple of 3 =?

Solution,

Total outcomes when 2 dice are rolled: (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)

Total possible outcomes = 36

The outcome in which the sum of the numbers is an odd number:   (1, 2) (1,4)(1, 6)(2, 1)(2, 3)(2, 5)(3, 2)(3, 4)(3, 6)(4, 1)(4, 3)(4, 5)(5, 2)(5, 4)(5, 6)(6, 1)(6, 3)(6, 5)

The total outcome with the sum of the numbers is an odd number = 18

The outcome in which the sum of the numbers is a multiple of 3: (1, 2)(1,5) (2, 1)(2, 4)(3, 3)(3, 6)(4, 2)(4, 5)(5, 1)(5, 4)(6, 3)(6, 6)

The common outcomes in which the sum of the numbers is an odd number and a multiple of 3: (1, 2) (2,1)(3,6)(4,5)(5,4)(6.3)

The probability that the sum of the numbers is an odd number and a multiple of 3 = 6 / 36

the probability that the sum of the numbers is an odd number and a multiple of 3 = 1 / 6

Hence, the probability that the sum of the numbers is an odd number and a multiple of 3 is 1 / 6.