Question

which outcome would allow asher to have a higher probability of winning the game? select three options. rolling a sum of 4 rolling a sum of 9 rolling a sum that is less than 5 rolling a sum that is greater than 5 but less than 7 rolling a sum that is greater than 9 but less than 11

Explanation:

Step1: Find total number of outcomes

When rolling two - six - sided dice, the total number of outcomes is \(n(S)=6\times6 = 36\).

Step2: Calculate number of outcomes for sum of 4

The possible combinations for a sum of 4 are \((1,3)\), \((2,2)\), \((3,1)\), so \(n(4)=3\). The probability \(P(4)=\frac{3}{36}=\frac{1}{12}\).

Step3: Calculate number of outcomes for sum of 9

The possible combinations for a sum of 9 are \((3,6)\), \((4,5)\), \((5,4)\), \((6,3)\), so \(n(9)=4\). The probability \(P(9)=\frac{4}{36}=\frac{1}{9}\).

Step4: Calculate number of outcomes for sum less than 5

The possible sums less than 5 are 2, 3, and 4. For sum = 2: \((1,1)\) (\(n(2) = 1\)); for sum = 3: \((1,2)\), \((2,1)\) (\(n(3)=2\)); for sum = 4: \(n(4)=3\). So \(n(<5)=1 + 2+3=6\), and \(P(<5)=\frac{6}{36}=\frac{1}{6}\).

Step5: Calculate number of outcomes for sum greater than 5 but less than 7

The possible sum is 6. The combinations are \((1,5)\), \((2,4)\), \((3,3)\), \((4,2)\), \((5,1)\), so \(n(6)=5\). The probability \(P(5 < sum<7)=\frac{5}{36}\).

Step6: Calculate number of outcomes for sum greater than 9 but less than 11

The possible sum is 10. The combinations are \((4,6)\), \((5,5)\), \((6,4)\), so \(n(10)=3\). The probability \(P(9 < sum<11)=\frac{3}{36}=\frac{1}{12}\).

Answer:

rolling a sum of 9, rolling a sum that is less than 5, rolling a sum that is greater than 5 but less than 7