8.1.1: Sample Spaces and Probability (Exercises)
SECTION 8.1 PROBLEM SET: SAMPLE SPACES AND PROBABILITY
In problems 1 - 6, write a sample space for the given experiment.
| 1) A die is rolled. | 2) A penny and a nickel are tossed. |
| 3) A die is rolled, and a coin is tossed. | 4) Three coins are tossed. |
| 5) Two dice are rolled. | 6) A jar contains four marbles numbered 1, 2, 3, and 4. Two marbles are drawn. |
In problems 7 - 12, one card is randomly selected from a deck. Find the following probabilities.
| 7) P( an ace) | 8) P( a red card) |
| 9) P( a club) | 10) P( a face card) |
| 11) P(a jack or a spade) | 12) P(a jack and a spade) |
For problems 13 - 16: A jar contains 6 red, 7 white, and 7 blue marbles. If one marble is chosen at random, find the following probabilities.
| 13) P(red) | 14) P(white) |
| 15) P(red or blue) | 16) P(red and blue) |
For problems 17 - 22: Consider a family of three children. Find the following probabilities.
| 17) P(two boys and a girl) | 18) P(at least one boy) |
| 19) P(children of both sexes) | 20) P(at most one girl) |
| 21) P(first and third children are male) | 22) P(all children are of the same gender) |
For problems 23 - 27: Two dice are rolled. Find the following probabilities.
| 23) P(the sum of the dice is 5) | 24) P(the sum of the dice is 8) |
| 25) P(the sum is 3 or 6) | 26) P(the sum is more than 10) |
| 27) P(the result is a double) (Hint: a double means that both dice show the same value) |
For problems 28-31: A jar contains four marbles numbered 1, 2, 3, and 4. Two marbles are drawn randomly WITHOUT REPLACEMENT. That means that after a marble is drawn it is NOT replaced in the jar before the second marble is selected. Find the following probabilities.
| 28) P(the sum of the numbers is 5) | 29) P(the sum of the numbers is odd) |
| 30) P(the sum of the numbers is 9) | 31) P(one of the numbers is 3) |
For problems 32-33: A jar contains four marbles numbered 1, 2, 3, and 4. Two marbles are drawn randomly WITH REPLACEMENT. That means that after a marble is drawn it is replaced in the jar before the second marble is selected. Find the following probabilities.
| 32) P(the sum of the numbers is 5) | 33) P(the sum of the numbers is 2) |