# Help me with probability please?

How would I solve these questions?!

Suppose that you roll a pair of fair dice.

a. What is the probability that the sum is at least 8?

b. What is the probability that the sum is not 7?

c. Given that you roll a sum of 7 on the first roll, what is the probability that you roll a sum of 7 on the second roll?

d. What is the probability that you roll a sum of 7 two times in a row?

Relevance

These are all relative frequency probability problems. First, you need to know that there are 36 possible outcomes. Imagine you roll a red die and a green one. For each value of the red die, there are 6 possible ones for the green one. Since the red die has 6 possible values, 6*6=36.

Here are the number of ways you can roll each number with 2 dice:

2, 12: 1 way (1,1 or 6,6)

3, 11: 2 ways (1,2; 2,1 or 5,6; 6,5) Remember that the red and green dice are different.

4, 10: 3 ways

5, 9 : 4 ways

6, 8 : 5 ways

7: 6 ways.

So the probability of rolling a 7 is 6/36 = 1/6. The probability of rolling a 6 or a 7 is (6+5)/36 = 11/36

And so on.

1. Sum is at least 8: Sum is 8,9,10,11,or12. Probability is (5+4+3+2+1)/36 = 15/36 = 5/12

2. Probability of 7 is 1/6, so probability of complement is 1-(1/6) = 5/6

3. 1/6: The two rolls are independent. The value of one does not effect the probability of any outcome ON THE SECOND ROLL. It will affect the probability of the outcome of the sum. For example, if you roll 2 on the first roll, there is 0 probability of rolling 15 as the total of two rolls.

4. Since the rolls are independent, the probability of them BOTH occurring is the product of their probabilities. VERY IMPORTANT: this is only true when the events are independent.

so 1/6 on the first roll, 1/6 on the second, so 1/36 all together.