Question

Dhani has 4 cards numbered 1 through 4. He removes 2 cards at random and adds their values.

What is the probability that the sum is less than or equal to 5?
7/12
2/3
3/5
3/4

Answer 1

`2/3`

Explanation:

The total number of sums (not distinct) is
`4\cdot 3=12`, because we're removing without replacement.

Count the sums that fit the stipulation (sum
`\leq` 5):

`1,2,\\2,1\\1,3\\3,1\\1, 4\\4, 1\\2, 3, \\3,2`

There are 8 sums that work. Therefore, the desired answer is
`(8)/(12)=\boxed{(2)/(3)}`