SOLUTION: Roll a pair of fair dice? Then, find the probability to get sum on the top surfaces is less than seven or an odd number?

Question 1115482: Roll a pair of fair dice? Then, find the probability to get sum on the top surfaces is less than seven or an odd number?
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Roll a pair of fair dice. Then, find the probability to get a sum on the top surfaces that is less than seven or an odd number.
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Less than 7: 2,3,4,5,6
Odd numbers: 3,5,7,9,11

It is the union of these two sets: S= { 2,3,4,5,6,7,9,11 } that is of interest.

To find the probability of getting a sum in S, we can look at S', the complement of S:
P(S) = 1-P(S')
S' = { 8, 10, 12 }

There are 36 possible outcomes on the roll of two dice.
There are 3 ways to get an 8: {5,3},{3,5}, {4,4}
There are 3 ways to get a 10: {4,6}, {5,5}, {6,4}
There is one way to get a 12: {6,6}

In all, S' has 7 ways of occurring, so P(S') = 7/36, and P(S) = 1-7/36 = 29/36.
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Ans: P{sum = 2,3,4,5,6,7,9, or 11} = (approx. 0.806).
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EDIT: Oh thanks tutor ikleyn, I missed 8 = 6+2 = 2+6, so that adds two to S' making P(S')= 9/36 and P(S)=27/36=3/4.

Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
Roll a pair of fair dice. Then, find the probability to get a sum on the top surfaces that is less than seven or an odd number.
======================================================
Less than 7: 2,3,4,5,6
Odd numbers: 3,5,7,9,11

It is the union of these two sets: S= { 2,3,4,5,6,7,9,11 } that is of interest.

To find the probability of getting a sum in S, we can look at S', the complement of S:
P(S) = 1-P(S')
S' = { 8, 10, 12 }

There are 36 possible outcomes on the roll of two dice.
There are 5 ways to get an 8: {6,2}, {5,3}, {4,4}, {3,5}, {2,6}
There are 3 ways to get a 10: {4,6}, {5,5}, {6,4}
There is one way to get a 12: {6,6}

In all, S' has 9 ways of occurring, so P(S') = 9/36, and P(S) = 1-9/36 = 3/4.
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Ans: P{sum = 2,3,4,5,6,7,9, or 11} = = 75%.

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