reduced fraction form

1. A bag contains 6 purple marbles, 7 azure marbles and 10 orange marbles. What is the chance of drawing a purple marble? If a purple marble is drawn then placed back into the bag, and a second marble is drawn, what is the probability of drawing an orange marble? Give solutions exactly in reduced fraction form.

2. A mini license plate for a toy car must consist of a one digit odd number followed by two letters. Each letter must be a J or K. Repetition of letters is permitted.
* Use the counting principle to determine the number of points in the sample space.
* Construct a tree diagram to represent this situation.
* List the sample space.
* Determine the exact probability of creating a mini license plate with a J. Give solution exactly in reduced fraction form.

3. A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting

* a three, given the card is a not a face card.
* a four, given the card is not a diamond.
* a Jack given the card is not a face card.

Show step by step work. Give all solutions exactly in reduced fraction form.

4. A bag contains a total of 20 batteries, of which four are defective. Selecting two at random, without replacement, determine the probability that none of the batteries you select are good.