Two balls are drawn at random without replacement from a box

Two balls are drawn at random, without replacement, from a box containing 10 balls enumerated 1, 2, 3... , 10. What is the probability that the sum of the drawn ball enumerations is equal to 5? Show the calculations and explain how you think.

Solution

There are 10C2 = 45 ways to choose any 2 balls (regardless of order)

There are only 2 ways to get a 5, that is, to get (1,4) and (2,3).

Thus,

P(sum is 5) = 2/45 or 0.044444444 [ANSWER]