A pair of fair dice is tossed. Find the probability that the maximum of the two numbers is greater than $4$.
My attempted solution:
$E=\{(1,5), (2,5), (3,5), (4,5), (5,5), (6,5),$
$(1,6), (2,6), (3,6), (4,6), (5,6), (6,6),$
$(5,1), (5,2), (5,3), (5,4), (5,6),$
$(6,1), (6,2), (6,3), (6,4), (6,5)\}$
Here $n_s = 22.$
So, $P =\frac{22}{36} = \frac{11}{18}.$
But, the correct answer is, $\frac{5}{9}$.
What am I missing?
in this case, it is certainly true that it is easiest to work with the complement.
- why is that? $\endgroup$