Question

what are the odds of rolling a sum of 5 with two die?
1 out of 6
1 out of 9
3 out of 7
2 out of 7

Explanation:

Step1: Find total number of outcomes

When rolling two dice, each die has 6 possible outcomes. So the total number of outcomes when rolling two dice is \(6\times6 = 36\).

Step2: Find number of ways to get a sum of 5

The possible combinations to get a sum of 5 are \((1,4)\), \((2,3)\), \((3,2)\), \((4,1)\), so there are 4 ways.

Step3: Calculate the probability

The probability \(P\) of getting a sum of 5 is the number of favorable outcomes divided by the total number of outcomes, \(P=\frac{4}{36}=\frac{1}{9}\).
The odds in favor of an event \(E\) is given by \(\frac{P(E)}{1 - P(E)}\). Here \(P(E)=\frac{1}{9}\), and \(1 - P(E)=1-\frac{1}{9}=\frac{8}{9}\). So the odds are \(\frac{\frac{1}{9}}{\frac{8}{9}}=\frac{1}{8}\) in favor. But if we consider odds as the ratio of favorable to non - favorable in a non - standard sense (favorable : non - favorable), favorable is 4 and non - favorable is \(36 - 4=32\), and the ratio simplifies to 1 out of 9.

Answer:

1 out of 9