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 StartFraction 6 over 36 EndFraction.

A table with 36 total outcomes.

Marta has a lower probability of winning than Elena has. Which could be the outcome that Marta needs to win the game? Select three options.
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

Count the ordered pairs (out of 36) that give each event and compare to Elena’s 6/36.

- sum of 7: 6 outcomes → 6/36 (equal to Elena) — not allowed.
- sum of 6: 5 outcomes → 5/36 (< 6/36) — allowed.
- sum of 2 or 9: 1 + 4 = 5 outcomes → 5/36 (< 6/36) — allowed.
- sum > 9: sums 10,11,12 → 3+2+1 = 6 outcomes → 6/36 (equal) — not allowed.
- sum > 2 but < 5 (sums 3 or 4): 2 + 3 = 5 outcomes → 5/36 (< 6/36) — allowed.

So the three possible outcomes for Marta are: sum of 6; sum of 2 or 9; sum greater than 2 but less than 5.