11.5b Probability In Counting

A small pond contains five catfish and four bluegill. If five fish are caught at random, what is the probability that all of them are catfish?

• 1/90

• 1/126

• 1/210

• 1/56

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A car dealership has ten cars in the lot. Unfortunately, the keys to the cars have been mixed up. The manager randomly grabs a key and tries to start a car. A salesman also randomly picks a different key and tries to start another car. What is the probability that both cars start?

• 1/84

• 1/66

• 1/1716

• 1/90

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A gardener has nine identical-looking tulip bulbs, of which four will produce yellow tulips and five will become pink. He randomly selects and plants four of them and then gives the rest away. When the flowers start to bloom, what is the probability that exactly two of them are yellow?

• 175/429

• 175/396

• 10/21

• 100/231

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A shipment of eleven smartphones contains seven with cracked screens. If sold in a random order, what is the probability that exactly five of the first seven sold have cracked screens?

• 35/143

• 21/55

• C) 189/572

• D) 100/231

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A technician is launching fireworks near the end of a show. Of the remaining fourteen fireworks, seven are blue and seven are red. If she launches eight of them in a random order, what is the probability that exactly five of them are blue ones?

• 35/143 ≈ 24.476%

• 882/2431 ≈ 36.281%

• 35/66 ≈ 37.879%

• 105/286 ≈ 36.713%

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A politician is about to give a campaign speech and is holding a stack of thirteen cue cards, of which the first 3 are the most important. Just before the speech, he drops all of the cards and picks them up in a random order. What is the probability that cards #1, #2, and #3 are still in order on the top of the stack?

• 1/1716 ≈ 0.058%

• 1/1287 ≈ 0.078%

• 1/1001 ≈ 0.1%

• 1/30 ≈ 3.333%

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You are dealt five cards from a standard and shuffled deck of playing cards. Note that a standard deck has 52 cards and four of those are kings. What is the probability that you'll have exactly three kings in your hand?

• 10/21 ≈ 47.619%

• 94/54145 ≈ 0.174%

• 490/1287 ≈ 38.073%

• 441/1144 ≈ 38.549%

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A car dealership has five cars in the lot. Unfortunately, the keys to the cars have been mixed up. The manager randomly grabs a key and tries to start a car. A salesman also randomly picks a different key and tries to start another car. What is the probability that both cars start?

• 1/792 ≈ 0.126%

• 1/20 ≈ 5%

• 1/15 ≈ 6.667%

• 1/30 ≈ 3.333%

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Rob and Jacob each purchase one raffle ticket. If a total of ten raffle tickets are sold and two winners will be selected, what is the probability that both Rob and Jacob win?

• 1/2730 ≈ 0.037%

• 1/45 ≈ 2.222%

• 1/165 ≈ 0.606%

• 1/120 ≈ 0.833%

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A chemistry lab requires students to identify chemical compounds by using various tests. Each student is given samples of three different compounds, labeled A, B, and C. Each student is also given a list of eight possible compounds. If a student does not perform the tests and randomly chooses three from the list, what is the probability that she guesses all three correctly?

• 1/990 ≈ 0.101%

• 1/3003 ≈ 0.033%

• 1/336 ≈ 0.298%

• 1/210 ≈ 0.476%

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