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## Homework Statement

A pair of dice is rolled once, what is the probability that neither a doublet nor the sum of 10 will appear

## Homework Equations

P(A) = 1 - P(A')

Demorgans law

(AUB)

^{c}= A

^{c}∩ B

^{c}

## The Attempt at a Solution

I know how to do the solution through brute force and listing out all the possible scenarios:

(1,1), (1,2), (1,3) ...... (6,6) and doing it like that. But i wanted a more algebraic approach so I tried this:

Let A = is a doublet

Let B = sum of dices is 10

so then what I am looking for is

P(A

^{c}U B

^{c})

and applying demorgans

P(A

^{c}U B

^{c}) = P(A∩B )

^{c}

using the law that A

^{c}= 1 - A

I got the final easy equation

1 - P(A ∩ B )

solving for this

P(A) = 6/36 ...........(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

P(B) = 3/36 ............(4,6), (5,5),(6,4)

plug in numbers

1 - (6/36)*(3/36) != the answer of 7/9

Apparently, math lies, j.k. Can someone let me know what i am doing wrong?