Question

What are the odds against obtaining an 11 when a pair of dice is tossed once?

Answer 1

Let's find our sample space first. There are $36$ equally likely outcomes:

$\left\{\right(1,1\left)\right(1,2\left)\right(1,3\left)\right(1,4\left)\right(1,5\left)\right(1,6),$

$(2,1)(2,2)(2,3)(2,4)(2,5)(2,6),$

$(3,1)(3,2)(3,3)(3,4)(3,5)(3,6),$

$(4,1)(4,2)(4,3)(4,4)(4,5)(4,6),$

$(5,1)(5,2)(5,3)(5,4)(5,5)(5,6),$

$(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)\}$

Now we find all the outcomes that match the desired result i.e obtaining a sum $11$:

$\left\{\right(5,6\left)\right(6,5\left)\right\}$ which is $\frac{2}{36}=\frac{1}{18}$