Roll two standard dice and add the numbers. What is the probability of getting a number larger that 9 for the first time on the third time.
It means that the first two times you get a 9 or less, but the third time you get a 10, 11 or 12.
For third time, add the probabilities from Bobpursley. For either-or probabilities, add individual probabilities.
(1/6*1/6) + (2*1/6*1/6) + (3*1/6*1/6) = ?
Probability of 9 or less = 1 -?
For probability of all events, multiply probabilities of individual events. Thus the answer to your problem is:
(1-?)(1-?)(?) = ??
I'll let you do the calculations.
larger than 9? that means 10,11, 12
Well, to get a 12, you can do it one way: Pr=1/6*1/6
To get an 11, you can do it two ways (5,6, or6,5) Pr= 2*1/6*1/6
To get a 10, you can do it 64,46,5,5 three ways
Pr=3*1/6*1/6
add the probabilities of all the combinations.
I seem to get 0.167--book has 0.1157
Thank you for trying--appreciate it.
To find the probability of getting a number larger than 9 for the first time on the third roll, we need to consider the possible outcomes and calculate the probability of each outcome.
When rolling two standard dice, the possible outcomes range from 2 (1 on each die) to 12 (6 on each die). We want to find the probability of getting a number larger than 9 for the first time on the third roll, which means we need to consider the probabilities of getting numbers less than or equal to 9 on the first and second rolls.
Let's break down the possibilities step by step:
1. First Roll:
- To get a number larger than 9, the sum of the numbers on the dice must be 10, 11, or 12.
- There are 3 possibilities to achieve this: (4, 6), (5, 5), and (6, 4).
- Therefore, the probability of rolling a number larger than 9 on the first roll is 3/36, or 1/12.
2. Second Roll:
- To calculate the probability of not rolling a number larger than 9 on the second roll, we need to consider the outcomes of the first roll. If we already rolled a number larger than 9, we don't need to worry about the second roll.
- We need to calculate the probability of getting a sum less than or equal to 9. We exclude the outcome (5, 5) because it is the only way to get exactly 10, which we want to avoid.
- There are 30 possible outcomes for the second roll: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5).
- Therefore, the probability of rolling a number less than or equal to 9 on the second roll is 30/36, or 5/6.
3. Third Roll:
- We already rolled a number less than or equal to 9 on the first and second rolls, so we need to calculate the probability of rolling a number larger than 9 only on the third roll.
- The possibilities for getting a sum larger than 9 are: (4, 6), (5, 5), and (6, 4).
- Therefore, the probability of rolling a number larger than 9 on the third roll is 3/36, or 1/12.
To find the probability of getting a number larger than 9 for the first time on the third roll, we need to multiply the probabilities of each step. Thus, the probability is (1/12) * (5/6) * (1/12) = 5/864.
Therefore, the probability of getting a number larger than 9 for the first time on the third roll is 5/864.