4.E: Probability Using Tree Diagrams and Combinations (Optional Exercises)
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SECTION 8.3 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.
|1) P( both red)||2) P(one red, one yellow)|
|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 8.3.2. Do not use combinations.
|5) P( All three red)||6) P(two red, one blue)|
|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.
|9) P(all three red)||10) P(two white and 1 blue)|
|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.
|13) At least three freshmen.||14) No sophomores.|
|15) All four of the same class.||16) Not all four from the same class.|
|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.
|19) Two hearts, two spades, and one club.||20) A flush of any suit (all cards of a single suit).|
|21) A full house of nines and tens (3 nines and 2 tens).||22) Any full house.|
23) A pair of nines and a pair of tens
|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:
|25) P(playlist has 2 songs of each type)||26) P(playlist has no country songs)|
|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.
|29) The committee has 2 engineers, 2 salespeople, and 1 customer service representative.||30) The committee contains 3 engineer and 2 salespeople.|
|31) The committee has no engineers.||32) The committee has all salespeople.|
Do the following birthday problems.
|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.|