Dice is a popular game in gambling casinos. Two dice are tossed, and various amounts are paid according to the outcome. In a certain game, if a four or eleven occurs on the first roll, the player wins. What is the probability of winning on the first roll?
4 = 2+2 or 3+1 or 1+3 = 3/36
11 = 6+5 or 5+6 = 2/36
Either-or probability is found by adding the individual probabilities.
To determine the probability of winning on the first roll in this dice game, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
In this case, the favorable outcomes are when a four or eleven occurs on the first roll. Let's analyze each number separately:
1. The number four can be obtained by rolling a 1 and a 3 or a 2 and a 2. So, there are two ways to get a four.
2. The number eleven can only be obtained by rolling a 5 and a 6 or a 6 and a 5. Therefore, there are two ways to get eleven.
Adding up the number of favorable outcomes, we have a total of four ways to win on the first roll.
Now, let's determine the total number of possible outcomes when two dice are tossed. Each die has six faces with numbers from 1 to 6, so there are six possible outcomes for each die. Since there are two dice, the total number of possible outcomes is 6 * 6 = 36.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 36
Probability = 1 / 9
Therefore, the probability of winning on the first roll in this game is 1/9.