Five balls, numbered 1, 2, 3, 4, and 5, are placed in a bin. Two balls are drawn at random without replacement. What is the probability that the sum of the numbers on the balls drawn is 7 ?

To solve this problem, we first need to determine all the possible pairs of balls that can be drawn and then identify which of these pairs sum to 7.

Step 1: Determine all possible pairs of balls Since we are drawing 2 balls without replacement from a set of 5, the total number of possible pairs is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial. Plugging in our values, we get C(5, 2) = 5! / [2!(5-2)!] = 10. So, there are 10 possible pairs of balls.

Step 2: Identify pairs that sum to 7 The pairs that sum to 7 are (2, 5), (3, 4), and (4, 3). So, there are 3 pairs that meet our criteria.

Step 3: Calculate the probability The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the probability that the sum of the numbers on the balls drawn is 7 is 3 (favorable outcomes) divided by 10 (total outcomes), or 0.3.