A bag contains 17 marbles: 10 purple and 7 green. The purple marbles are numbere

Question

A bag contains 17 marbles: 10 purple and 7 green. The purple marbles are numbered 1 through 10 and the green ones are numbered 11 through 17. If one marble is chosen, what is the probability that it is purple? If one marble is chosen, what is the probability that it is green? If one marble is chosen, what is the probability that it is both purple and even? If one marble is chosen, what is the probability that it is NOT both purple and even? If one marble is chosen, what is the probability that it is green or even? If one marble is chosen, what is the probability it is even, given that it is green? If two marble are chosen with replacement, what is the probability both are odd? If two marble are chosen without replacement what is the probability that the first is purple and the second is green? Give an example of two events that are mutually exclusive when one marble is chosen. If 89 marbles are chosen at random without replacement, what is the probability that at least one is purple?

Explanation / Answer

As specifically asked, only Q13 is answered.

Let the event A be that the marble selected is purple and B be the event that the marble selected is green.

Then, A and B are mutually exclusive because if A happens B cannot happen and vice-versa. i.e., both A and B cannot occur simultaneously since only one ball is selected.

Yet another example: event A be that the marble selected has an even number on it and B  be the event that the marble selected has an odd number on it.  

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