6.3E: Exercises - Probability Using Tree Diagrams and Combinations
PROBLEM SET: PROBABILITIES USING TREE DIAGRAMS AND COMBINATIONS
Two apples are chosen from a basket containing five red and three yellow apples.
Draw a tree diagram below, and find the following probabilities.
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1) P( both red) |
2) P(one red, one yellow) |
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3) P(both yellow) |
4) P(First red and second yellow) |
A basket contains six red and four blue marbles. Three marbles are drawn at random.
Find the following probabilities using the method shown in
Example 6.3.2
. Do not use combinations.
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5) P( All three red) |
6) P(two red, one blue) |
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7) P(one red, two blue) |
8) P(first red, second blue, third red) |
Three marbles are drawn from a jar containing five red, four white, and three blue marbles.
Find the following probabilities using combinations.
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9) P(all three red) |
10) P(two white and 1 blue) |
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11) P(none white) |
12) P(at least one red) |
A committee of four is selected from a total of 4 freshmen, 5 sophomores, and 6 juniors. Find the probabilities for the following events.
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13) At least three freshmen. |
14) No sophomores. |
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15) All four of the same class. |
16) Not all four from the same class. |
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17) Exactly three of the same class. |
18) More juniors than freshmen and sophomores combined. |
Five cards are drawn from a deck. Find the probabilities for the following events.
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19) Two hearts, two spades, and one club. |
20) A flush of any suit ( all cards of a single suit ). |
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21) A full house of nines and tens ( 3 nines and 2 tens ). |
22) Any full house. |
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23) A pair of nines and a pair of tens
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24) Any two pairs ( two cards of one value, two more cards of another value, and the fifth card does not have the same value as either pair ). |
Jorge has 6 rock songs, 7 rap songs and 4 country songs that he likes to listen to while he exercises.
He randomly selects six (6) of these songs to create a playlist to listen to today while he exercises.
Find the following probabilities:
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25) P(playlist has 2 songs of each type) |
26) P(playlist has no country songs) |
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27) P(playlist has 3 rock, 2 rap, and 1 country song) |
28) P(playlist has 3 or 4 rock songs and the rest are rap songs) |
A project is staffed 12 people: 5 engineers, 4 salespeople, and 3 customer service representatives.
A committee of 5 people is selected to make a presentation to senior management.
Find the probabilities of the following events.
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29) The committee has 2 engineers, 2 salespeople, and 1 customer service representative. |
30) The committee contains 3 engineer and 2 salespeople. |
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31) The committee has no engineers. |
32) The committee has all salespeople. |
Do the following birthday problems.
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33) If there are 5 people in a room, what is the probability that no two have the same birthday? |
34) If there are 5 people in a room, find the probability that at least 2 have the same birthday. |