6.1E: Exercises - Sample Spaces and Probability
PROBLEM SET: SAMPLE SPACES AND PROBABILITY
In problems 1 - 6, write a sample space for the given experiment.
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1) A die is rolled. |
2) A penny and a nickel are tossed. |
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3) A die is rolled, and a coin is tossed. |
4) Three coins are tossed. |
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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.
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7) P( an ace) |
8) P( a red card) |
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9) P( a club) |
10) P( a face card) |
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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.
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13) P(red) |
14) P(white) |
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15) P(red or blue) |
16) P(red and blue) |
For problems 17 - 22: Consider a family of three children. Find the following probabilities.
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17) P(two boys and a girl) |
18) P(at least one boy) |
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19) P(children of both sexes) |
20) P(at most one girl) |
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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.
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23) P(the sum of the dice is 5) |
24) P(the sum of the dice is 8) |
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25) P(the sum is 3 or 6) |
26) P(the sum is more than 10) |
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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.
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28) P(the sum of the numbers is 5) |
29) P(the sum of the numbers is odd) |
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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.
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32) P(the sum of the numbers is 5) |
33) P(the sum of the numbers is 2) |