11.5a Probability with Counting

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

• 1/30

• 1/66

• 1/715

• 1/220

A child is drawing a rainbow using a box of seventeen different colored crayons, which include the seven required colors. After drawing the red, orange, yellow, and green arcs in the proper order, she forgets the last three colors. From the remaining thirteen crayons, she chooses three at random to finish drawing the rainbow. What is the probability that she correctly finishes the ROYGBIV rainbow?

• 1/2730 ≈ 0.037%

• 1/120 ≈ 0.833%

• 1/286 ≈ 0.35%

• 1/1716 ≈ 0.058%

A mechanic working under a car requires three different size wrenches from his toolbox, which contains thirteen different wrenches. Reaching for his toolbox, he grabs three of them at random. What is the probability that the mechanic has all of the wrenches he needs?

• 1/286 ≈ 0.35%

• 1/210 ≈ 0.476%

• 1/1716 ≈ 0.058%

• 1/15 ≈ 6.667%

A politician is about to give a campaign speech and is holding a stack of eleven 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?

• 1/132 ≈ 0.758%

• 1/990 ≈ 0.101%

• 1/3003 ≈ 0.033%

• 1/56 ≈ 1.786%

There are sixteen songs on your playlist. With random shuffle and no repetition, you listen to two songs. What is the probability that you listened to your favorite song first and your least favorite song second?

• 1/240 ≈ 0.417%

• 1/1320 ≈ 0.076%

• 1/792 ≈ 0.126%

• 1/120 ≈ 0.833%

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

• (175/429) ≈ 40.793%

• (14/33) ≈ 42.424%

• (35/143) ≈ 24.476%

• (5/11) ≈ 45.455%

A class has six boys and eight girls. If the teacher randomly picks seven students, what is the probability that he will pick exactly four girls?

• (175/429) ≈ 40.793%

• (189/572) ≈ 33.042%

• (25/66) ≈ 37.879%

• (18/35) ≈ 51.429%