Finite Math: Probability

Question

A container has nine marbles numbered 1, 2, 3, 4, 5, 6, 7, 8, 9. Two different marbles are selected at random from this container.

(a) What is the probability that one of the marbles selected was “7” ?

(b) What is the probability that the sum is 8?

Answer 1

Since there are 9 marbles, and you are drawing without replacement, there is a 2 out of 9 chance that you will select a 7 in two draws. There are many ways to reason this out.

If we disregard order of selection:

There are 8 ways to select a 7 and one of the other 8 numbers.

There are C(9,2) = 36 possible pairs.

Then, the probability of having a pair with a 7 is 8/36 = 2/9

Another way: as you are drawing twice, the sum of the expected number for all possible number values is 2; yet, this is the sum across 9 numbers, so the probability of each is 2/9 for each value.

Now for the second question, you can have a sum of 8 with 1, 7; 2, 6; and 3;5

Then, the probability of having the dice sum to 8 is 3/36 = 1/12