If you roll a pair of dice, what is the probability of rolling either a single 5 or a sum that is an even number?

1 Answer
Oct 28, 2015

#2/3#

Explanation:

Note that total number of possible cases are #6^2= 36#

Getting a single #5# ( Say event #A# ) means situation like as #(1,5),(2,5),(3,5),(4,5),(6,5),(5,1),(5,2),(5,3),(5,4),(5,6)# i.e. #10# cases and we have #18# cases when sum is an even number ( Say event #B# ) . But these two events are not mutually exclusive. Here #(1,5),(3,5),(5,1),(5,3)# i.e. #4# cases where we get a single #5# as well as sum is a even number ( Say event #A nn B# ) .

So we have number of favorable cases to our event #= n(A)+n(B)-n(A nn B) = 10+18-4=24#

So required probability #= 24/36=2/3#