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 twelve or five occurs on the first roll, the player wins. What is the probability of winning on the first roll?
1
0
The first dice generates a random integer between 1 and 6, and the second one does likewise - which gives 36 possible outcomes, all of which are equally likely if you distinguish between the two dice. Of these, how many total 5 or 12? There's only one way to get 12, namely that both dice come up six; however there are four different ways to get a total of 5, namely (1 & 4), (2 & 3), (3 & 2) and (4 & 1) for the first and second dice respectively. All of these outcomes are equally likely and are mutially exclusive, so all you have to do is add up the total number of them. That's (1 + 4) = 5 out of 36. 5/36 = 0.139, which is the answer.
To calculate the probability of winning on the first roll in the game, we need to determine the number of favorable outcomes (i.e., when a twelve or five occurs) and divide it by the total number of possible outcomes when rolling two dice.
Total number of possible outcomes when rolling two dice:
There are 6 possible outcomes for each of the two dice (since each die has 6 faces). Therefore, the total number of possible outcomes is 6 * 6 = 36.
Number of favorable outcomes:
To win on the first roll, we need either a twelve or a five to occur. Let's determine how many outcomes result in a twelve or a five:
- The outcome (6, 6) results in a twelve.
- The outcomes (1, 4), (2, 3), (3, 2), and (4, 1) result in a five.
Counting these outcomes, there are 6 favorable outcomes.
Probability of winning on the first roll:
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 = 6 / 36 = 1/6
Therefore, the probability of winning on the first roll in the game is 1/6.
To find the probability of winning on the first roll in this dice game, we need to determine the number of favorable outcomes (outcomes where the player wins) and the total number of possible outcomes (all possible combinations when rolling two dice).
First, let's find the number of favorable outcomes, which in this case are getting a sum of twelve or five on the two dice.
To get a sum of twelve, we can have the following combinations: (6, 6). So, there is 1 favorable outcome for getting a sum of twelve.
To get a sum of five, we can have the following combinations: (1, 4), (2, 3), (3, 2), and (4, 1). So, there are 4 favorable outcomes for getting a sum of five.
Now, let's find the total number of possible outcomes. When two dice are rolled, the total number of outcomes is given by multiplying the number of outcomes on each die. Since each die has 6 sides, there are 6 outcomes for each die. Therefore, the total number of possible outcomes is 6 x 6 = 36.
To calculate the probability of winning on the first roll, 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 = (1 + 4) / 36
Probability = 5 / 36
Therefore, the probability of winning on the first roll in this game is 5/36.