this is real hard and i would love some help.
In a game of craps, a player rolls 2 balanced dice. There are 36 equally likely outcomes. What is the probability that:
a) the sum is either 3 or 8
b) the sum is 6 or doubles rolled
c) the sum is 6 AND doubles
d) the sum is 6 and both numbers are odd
please help
If there are 36 possible outcomes, you are always dividing by 36.
For A, you can get 4 possibilities:
2,1
1,2
6,2
2,6
There are no other ways the dice will total 3 or 8.
The other problems can be solved by similar logic.
I hope this helps. Thanks for asking.
I'd be happy to help you with these probability questions in the game of craps! Let's break them down one by one and explain how to get the answers.
a) The probability that the sum is either 3 or 8:
To find the probability, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
For the sum 3, there is only one combination: (1, 2). For the sum 8, there are two combinations: (2, 6) and (3, 5). So, the total number of favorable outcomes is 1 (for the sum 3) + 2 (for the sum 8) = 3.
Since there are 36 equally likely outcomes when rolling two dice, the probability of getting a sum of 3 or 8 is 3/36, which simplifies to 1/12.
b) The probability that the sum is 6 or doubles are rolled:
Again, we need to count the favorable outcomes and divide by the total outcomes.
For the sum 6, there are five combinations: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). For doubles, there are six combinations: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6). So, the total number of favorable outcomes is 5 (for the sum 6) + 6 (for doubles) = 11.
Therefore, the probability of getting a sum of 6 or rolling doubles is 11/36.
c) The probability that the sum is 6 AND doubles are rolled:
To find the probability, we need to determine the number of favorable outcomes where both conditions are satisfied.
From the previous question, we know that there are six combinations where doubles are rolled. However, only one of these combinations results in a sum of 6, which is (3, 3). Therefore, the number of favorable outcomes is 1.
Thus, the probability of rolling a sum of 6 and doubles is 1/36.
d) The probability that the sum is 6 and both numbers are odd:
This question requires both numbers being odd and their sum being 6.
The combinations that satisfy this condition are (1, 5) and (5, 1). So, there are two favorable outcomes.
Hence, the probability of rolling a sum of 6 with both numbers being odd is 2/36, which reduces to 1/18.
I hope this explanation was helpful to you! Let me know if you have any further questions.