Question

In a box there are nine identical marbles. Four of these marbles are red and five are not. Adam is blindfolded and selects two marbles. What is the probability that Adam selects at least one red marble?

Answer

Let's first find probability that Adam doesn't select red marble.

First selection: there are `9` marbles, `5` of which are not red. Therefore, probability of selecting non-red marble is `5/9`.

Second selection: since we've selected non-red marble at the first step, then there are `8` marbles, `4` of which are not red. Therefore, probability of selecting non-red marble at the second step is `4/8=1/2`.

By the product rule, probability of selecting two non-red marbles is `5/9*1/2=5/18`.

Finally, probability that at least one marble is red is `1` minus probability of selecting two non-red marbles: `1-5/18=13/18`.

Answer: `13/18` .