Question

A pair of dice are rolled, and the dots are counted. You bet $1. If 5 or 10 come up, you win $3 (payoff odds are 3 to 1). If anything else comes up, you lose your $1 bet. Find:

Question: What is the probability of winning this bet?

Answer 1

The probability of winning the bet by rolling a sum of 5 or 10 with two dice is 7/36, which is approximately 0.1944 when rounded to four decimal places.

Step-by-step explanation:

To calculate the probability of winning the bet when rolling two dice and getting a sum of either 5 or 10, we first identify the possible outcomes that result in a sum of 5 or 10. We can roll a 5 with the following combinations: (1,4), (2,3), (3,2), (4,1), which gives us 4 possibilities. For a sum of 10, the possibilities are: (4,6), (5,5), (6,4), which gives us 3 possibilities. The total number of outcomes when rolling two dice is 6 x 6 = 36.

Thus, the probability of winning is the number of winning outcomes divided by the total number of outcomes, which is (4 + 3) / 36, or 7/36. To present this accurately, we convert it to a decimal and round to four decimal places as requested, yielding approximately 0.1944.