Archie rolls two number cubes, each with sides numbered 1 through 6. He finds the sum of the numbers on the tops of the cubes. What two sums have the same probability?

A. 3 and 4
B. 5 and 9
C. 5 and 8
D. 10 and 12

Ω = {( x ; y ) : x ; y ∈ { 1 ; 2 ; 3 ; 4 ; 5 ; 6 }} Ω = 6 2 = 36 A = {( 1 ; 2 ) ; ( 2 ; 1 ) ; ( 1 ; 3 ) ; ( 3 ; 1 ) ; ( 2 ; 2 )} ; A = 5 ; P ( A ) = 36 5 ​ B = {( 1 ; 4 ) ; ( 4 ; 1 ) ; ( 2 ; 3 ) ; ( 3 ; 2 ) ; ( 3 ; 6 ) ; ( 6 ; 3 ) ; ( 4 ; 5 ) ; ( 5 ; 4 )} ; B = 8 ; P ( B ) = 36 8 ​ C = {( 1 ; 4 ) ; ( 4 ; 1 ) ; ( 2 ; 3 ) ; ( 3 ; 2 ) ; ( 2 ; 6 ) ; ( 6 ; 2 ) ; ( 3 ; 5 ) ; ( 5 ; 3 ) ; ( 4 ; 4 )} C = 9 ; P ( C ) = 36 9 ​
D = {( 4 ; 6 ) ; ( 4 ; 6 ) ; ( 5 ; 5 ) ; ( 6 ; 6 )} ; D = 4 ; P ( D ) = 36 4 ​
A . 3 → ( 1 ; 2 ) ; ( 2 ; 1 ) → 36 2 ​ 4 → ( 1 ; 3 ) ; ( 3 ; 1 ) ; ( 2 ; 2 ) → 36 3 ​ B . 5 → ( 1 ; 4 ) ; ( 4 ; 1 ) ; ( 2 ; 3 ) ; ( 3 ; 2 ) → 36 4 ​ 9 → ( 3 ; 6 ) ; ( 6 ; 3 ) ; ( 4 ; 5 ) ; ( 5 ; 4 ) → 36 4 ​
C . 5 → ( 1 ; 4 ) ; ( 4 ; 1 ) ; ( 2 ; 3 ) ; ( 3 ; 2 ) → 36 4 ​ 8 → ( 2 ; 6 ) ; ( 6 ; 2 ) ; ( 3 ; 5 ) ; ( 5 ; 3 ) ; ( 4 ; 4 ) → 36 5 ​ D . 10 → ( 4 ; 6 ) ; ( 6 ; 4 ) ; ( 5 ; 5 ) → 36 3 ​ 12 → ( 6 ; 6 ) → 36 1 ​

Answered by Anonymous | 2024-06-10

The same probability *
Write firstly what results it's able to get and their sum: .....1....2.....3.....4....5.....6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12
As you can see there are four options to get "5" and also four options to get "9". So the B is proper answer. Sum 5 and sum 9 have the same probability.

Answered by marmal | 2024-06-10

The two sums that have the same probability when rolling two dice are 5 and 9, both with a probability of \frac{1}{9}.
;

Answered by Anonymous | 2024-10-02