Suppose that in a particular game two dice are tossed, and various amounts are paid according to the outcome. Find the requested probability. (Enter the probability as a fraction.) If a seven or an eight occurs on the first roll, the player wins. What is the probability of winning on the first roll?
thank you
36 possible outcomes if order matters
If it is the sum that matters you have to figure a different probability for every sum
for example there are 4 ways of getting a sum of 5
1+4 or 4+1
2+3 or 3+2
to get a sum of 6 though, there are 5 ways
1+5 or 5+1
2+4 or 4+2
3+3
On the first roll
get 7 with
1+6 or 6+1
2+5 or 5+2
3+4 or 4+3
four ways so 4/36 = 1/9
get 8 with
2+6 or 6+2
3+5 or 5+3
4+4
five ways so 5/36
1/9 + 5/36 = 9/36 = 1/4 = chance of winning on first roll
thank you
To find the probability of winning on the first roll, we need to determine the favorable outcomes (rolls that result in a seven or an eight) and the total possible outcomes (all possible combinations of the dice rolls).
First, let's determine the favorable outcomes:
- There are 6 ways to roll a seven: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
- There are 5 ways to roll an eight: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
Therefore, there are 6 + 5 = 11 favorable outcomes.
Next, let's determine the total number of possible outcomes:
Since there are two dice being rolled, each die can show a number from 1 to 6. So, the total number of possible outcomes is 6 * 6 = 36.
Now, to find the probability, we divide the favorable outcomes by the total outcomes:
Probability of winning on the first roll = favorable outcomes / total possible outcomes
Probability of winning on the first roll = 11 / 36
Therefore, the probability of winning on the first roll is 11/36.
To find the probability of winning on the first roll when two dice are tossed, we need to determine the number of favorable outcomes (winning outcomes) and the total number of possible outcomes.
First, let's determine the number of winning outcomes. We need to find the combinations of dice roll results that will result in a sum of either seven or eight. The possible combinations are:
- For seven: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) --> 6 combinations
- For eight: (2,6), (3,5), (4,4), (5,3), (6,2) --> 5 combinations
Therefore, there are a total of 6 + 5 = 11 winning outcomes.
Next, let's determine the total number of possible outcomes when two dice are rolled. Each die can have 6 possible outcomes, so the total number of outcomes is 6 * 6 = 36.
Finally, we can calculate the probability of winning on the first roll by dividing the number of winning outcomes by the total number of possible outcomes:
Probability of winning on the first roll = Number of winning outcomes / Total number of possible outcomes
= 11 / 36
Thus, the probability of winning on the first roll in this game is 11/36.
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