#2 A single die is rolled three times. Determine the probability that the sum virus of the three rolls is less than 100 given that the first roll is a 76. You must show all of your work for full marks

7 months ago

Answered By Leonardo F

Given that the first roll was already a 6, and we want for the sum of all three rolls to be less than 10, it makes sense that the sum of the second and third rolls must be less than 4. Let's analyze all of the possibilities in which the sum of the second and third rolls is less than 4:

2nd Roll 3rd Roll SUM

1 2 3

2 1 3

1 1 2

Since a die cannot roll a 0, there are only three possibilities in which the sum of the second and third rolls is less than 4. Now, let's count the total possible number of results of the second and third rolls. Since a die can roll a number from 1 to 6, there are 6 possibilities for each roll. So, for two rolls:

6 x 6 = 36

So there are 36 possible results. Since the probability is the ratio between the number of favorable results and the number of possible results, the probability will be:

7 months ago

## Answered By Leonardo F

Given that the first roll was already a 6, and we want for the sum of all three rolls to be less than 10, it makes sense that the sum of the second and third rolls must be less than 4. Let's analyze all of the possibilities in which the sum of the second and third rolls is less than 4:

2nd Roll 3rd Roll SUM

1 2 3

2 1 3

1 1 2

Since a die cannot roll a 0, there are only three possibilities in which the sum of the second and third rolls is less than 4. Now, let's count the total possible number of results of the second and third rolls. Since a die can roll a number from 1 to 6, there are 6 possibilities for each roll. So, for two rolls:

6 x 6 = 36

So there are 36 possible results. Since the probability is the ratio between the number of favorable results and the number of possible results, the probability will be:

P (SUM < 10) = 3/36 = 1/12

P (SUM < 10) = 0.0833 = 8.33 %