Question

conditional probability and independent events

if two die are rolled(36 outcome sample space) find probability of rolling the given events

A sum of 8, given the sum was greater than 7

P(sum8/greater than 7)

Answer 1

So, you are looking for th eprobability of 8+9+10+11+12

Answer 2

that's given the sum was greater than 7

Answer 3

The "given" part reduces the sample space.

Answer 4

now divide the prob of getting a sum of 8 by given the sum was greater than 7

Answer 5

P8/(P8+P9+P10+P11+P12)

Answer 6

There are 36 total ways to roll 2 dice, but "given the sum is greater than 7" means we're not even considering more than half of those. Let's figure out specifically how many cases that includes first.

Answer 7

wait...its asking what is the probability of getting a sum of 8, like 2,6-5,5-4,4-3,5- and the sum is also greater than 7

Answer 8

wait not 5,5

Answer 9

Number of way the sum can be 8:
6,2
2,6
5,3
3,5
4,4
Five ways
Number of ways the sum can be 9:
6,3
3,6
5,4
4,5
Four ways
Number of ways the sum can be 10:
6,4
4,6
5,5
Three ways
Number of ways the sum can be 11:
6,5
5,6
Two ways
Number of ways the sum can be 12:
6,6
One way

Answer 10

The probability will be:
(Number of rolls higher than 8) /(Number of rolls higher than 7)

Answer 11

so for a sum greater than 7 would it be 1 out of 15?

Answer 12

How many ways can you roll a sum greater than 7?

Answer 13

15

Answer 14

Right. How many ways can you roll a sum greater than 8?

Answer 15

6

Answer 16

Oh, really? Check again.

Answer 17

oh 10

Answer 18

so would you add 10 and 15 than divide that by 36?

Answer 19

Nope.

Answer 20

15 tells you how many ways you can roll higher than 7, that's your universe, the possible outcomes you're considering.
10 tells you which of those possible outcomes you will call a "good" result.

Probability = "good"/total

Answer 21

so 10/36?

Answer 22

or 10/15?

Answer 23

The "good" results are 10. Since they say "given that the sum is over 7," that means that the total is smaller. We know that everything 7 and under didn't happen, so the total is smaller. Only 15.

Answer 24

so the answer would be 10/15?
is that correct?

Answer 25

yessir

Answer 26

ok thanks man.

Answer 27

do you think you can help me with another question?