Question

Two dice are thrown at same time, write down all the possible outcomes. What is the probability of (1) doublet 2. Prime doublet 3. Even doublet

Answer 1

Dear student
Sample space
{(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) }
The outcomes (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6) are called doublets.
Prime doublets are (2,2), (3,3), (5,5)
Even doublets are (2,2), (4,4), (6,6)
1. P(doublet) = 6/36 = 1/6
2. P(prime doublet) = 3/36 = 1/12
3. P(even doublet) = 3/36 = 1/12
Regards