Practice Problems for Probability Test

Discussion: Theoretical vs. Experimental

Fair vs. Unfair

And/or

Mutually exclusive vs. Mutually inclusive

1) Which of the following illustrates working with compound events? A) rolling a die B) tossing 2 coins C) drawing one card D) choosing one person

2) A standard deck of 52 cards is shuffled.  What is the probability of choosing the 5 of diamonds?

3) A die is rolled.  What is the probability that the number is even and less than 4?

4)A die is rolled.  What is the probability that the number rolled is greater than 2 and even?

5) A standard deck of cards is shuffled and one card is drawn.  Find the probability that the card is a queen or an ace.

6) A pair of dice are rolled. What is the probability of not rolling doubles? Are these events mutually exclusive?

7) A pair of dice is rolled.  What is the probability that the sum of the numbers rolled is either 7 or 11?

8) A drawer contains 3 red paperclips, 4 green paperclips, and 5 blue paperclips.  One paperclip is taken from the drawer and then replaced.  Another paperclip is taken from the drawer.  What is the probability that the first paperclip is red and the second paperclip is blue?9) A pair of dice is rolled. Two possible events are rolling a number greater than 8 and rolling an even number. Are these two events mutually exclusive events?

10) A pair of dice is rolled. A possible event is rolling a multipleof 5.  What is the probability of the complement of this

event?

11) A paper bag contains 15 slips of paper.  Eight of them areblue and are numbered from 1 to 8.  Seven of them are pinkand are numbered from 1 to 7. What is the probability ofdrawing a slip of paper with an even number?

12) If ice cream sundaes come in 5 flavors with 4 possible toppings, how many different sundaes can be made with one flavor of ice cream and one topping?  

13) A coin is tossed five times.  How many arrangements of heads and tails are possible?

14) Alarm clocks are sold in blue or pink with either digital or standard displays.  How many different arrangements of alarm clocks are possible?  List the sample space.

15) A movie theater sells 3 sizes of popcorn (small, medium, and large) with 3 choices of toppings (no butter, butter, extra butter).  How many possible ways can a bag of popcorn be purchased?

16) A password requires 3 letters and 2 numbers followed by a constant. If the letters are not case sensitive and the digits 0-9 can be used for the numbers, how many combinations of passwords can be made?