Question

Rolling a Red and Yellow Dice

(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)

A red die and a yellow die are rolled. The outcome "3 on the red die and 4 on the yellow die" can be represented by the ordered pair (3,4). What is the probability that the sum of the die is lucky number 7?

1/2

5/6

1/9

1/6

Answer 1

1/6

Explanation:

The total number of possible outcomes 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) = 36

The possible outcomes with sum 7 from the sample space are:

(1,6)(2,5)(3,4)(4,3)(5,2)(6,1) = 6

The probability with the sum 7 is:
`(Desired Outcomes)/(Possible Outcomes) = (6)/(36)`

=>
`(1)/(6)`

Hence the last option is correct.