Question

To win the game, Elena has to roll an even number first and a number less than 3 second. Her probability of winning is 6/36.

Marta has a lower probability of winning than Elena has. Which could be the outcome that Marta needs to win the game? Check all that apply.

rolling a sum of 7

rolling a sum of 6

rolling a sum of 2 or a sum of 9

rolling a sum that is greater than 9

rolling a sum that is greater than 2 but less than 5

Answer 1

B. rolling a sum of 6

C. rolling a sum of 2 or a sum of 9

E. rolling a sum that is greater than 2 but less than 5

Explanation:

Answer 2

• Prob (Marta winning) < Prob (Elena winning) : Case 1st, 3rd & 5th
• Prob (Marta winning) = Prob (Elena winning) : Case 2nd
• Prob (Marta winning) > Prob (Elena winning) : Case 4th

Explanation:

Elena outcomes of winning, first even no. & second no. = 3 : (2,1) , (2,2) , (4,1) , (4,2) , (6,1) , (6,2). So, Probability (Elena willing) = favourable outcomes / total outcomes = 6 / 36

• Margie dice sum '7' outcomes = (2,5) , (5,2) , (3,4) , (4,3). So, Prob = 4/36
• Margie dice sum '6' outcomes = (1,5) , (5,1) , (2,4) , (4,2) , (3,3). So, Prob = 6/36
• Margie dice sum '2' or '9' outcomes = (1,1) , (3,6) , (6,3) , (4,5) , (5,4). Prob = 5/36
• Margie dice sum '>9' outcomes = (3,6) , (6,3) , (4,5) , (5,4) , (4,6) , (6,4) , (5,5) , (5,6) , (6,5) , (6,6). Prob = 10/36
• Margie dice sum '>2,<5' outcomes = (1,2) , (2,1) , (2,2) , (1,3) , (3,1) = 4/ 36