Find the probability that the sum is as stated when a pair of dice is rolled.
A.4 or 11 or doubles
B. 8,given that the sum is greater than 4.
C.Even,given that the sum is greater than 4.
A. 4 can be obtained by 1&3, 3&1 or 2&2. 11 can only be obtained by 5&6 or 6&5. Doubles are 1&1, 2&2, 3&3, 4&4, 5&5 or 6&6. Since 2&2 occurs in two categories, only use it once to determine probability. Each of these has a 1/36 probability with two die. With "either-or" probabilities, you need to add the probabilities of the individual events.
B. This is confusing. To obtain 8, the sum of the die would always be greater than four. Are the data in error?
If it is 8 or given that the sum is greater than 4, you need to determine the combinations to get 5, 6, 7, 8, 9, 10, 11 or 12 to calculate your probability. Since 8 is in both categories, it only needs to be used once.
C. Assuming that the indivudal die do not need to be even, you need to figure the combinations that give you 6, 8, 10 and 12 to calculate the total probability from there.
I hope this helps. Thanks for asking.
A. To find the probability of getting either a sum of 4, 11, or doubles when rolling a pair of dice, you need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
For a sum of 4: There are 3 possible combinations (1&3, 3&1, or 2&2) that result in a sum of 4.
For a sum of 11: There are 2 possible combinations (5&6 or 6&5) that result in a sum of 11.
For doubles: There are 6 possible combinations (1&1, 2&2, 3&3, 4&4, 5&5, or 6&6) that result in doubles.
Since 2&2 is included in both the "sum of 4" and "doubles" categories, we only count it once.
The total number of possible outcomes when rolling a pair of dice is 6*6 = 36 (each die has 6 possible outcomes).
So, the probability of getting a sum of 4, 11, or doubles is (3+2+5) / 36 = 10/36 = 5/18.
B. It seems there is a contradiction in the question. If the sum is always greater than 4 to obtain 8, then the probability is 1, since it is a certainty. However, if the question is asking for the probability of obtaining an 8 given that the sum is greater than 4, we need additional information, such as the probabilities of the individual sums greater than 4.
C. Assuming the question is asking for the probability of getting an even sum given that the sum is greater than 4. We need to determine the combinations that result in even sums (6, 8, 10, or 12) when rolling a pair of dice.
For a sum of 6: There are 5 possible combinations (1&5, 2&4, 3&3, 4&2, or 5&1) that result in a sum of 6.
For a sum of 8: There are 5 possible combinations (2&6, 3&5, 4&4, 5&3, or 6&2) that result in a sum of 8.
For a sum of 10: There are 3 possible combinations (4&6, 5&5, or 6&4) that result in a sum of 10.
For a sum of 12: There is 1 possible combination (6&6) that results in a sum of 12.
The total number of possible outcomes when rolling a pair of dice is still 36.
So, the probability of getting an even sum given that the sum is greater than 4 is (5+5+3+1) / 36 = 14/36 = 7/18.