Probability question (tree diagram) question I am stuck on! (1 Viewer)

[narges-ts]

A deck contains six cards labelled the numbers 0,1,2,2,3 and 3. Ann draws two cards at random without replacement.

(i) find the probability that the sum of the two cards equal 5

(ii) find the probability that the sum of the two cards in less than 5


Ok so i got the first answer, but with the second question I only know how to answer it the long way by adding all the fractions together but the answer sheet has a short method that is kinda difficult to follow. Can someone please explain.

ANS: (i)= 4/15 (ii)=2/3

 

[pikachu975]

P(<5) = 1 - P(5 or more)

There are these cases for 5 or more: 23, 23, 32, 32, 33 which is 5.
The total cases are 6C2 = 15

P(<5) = 1 - 5/15 = 2/3