A jar contains 3 red, 2 blue, and 8 green marbles.
If one marble is drawn at random from the jar, what's the probability that marble is green?
If two marbles are drawn at random from the jar, with the first marble being replaced before the second is drawn, what's the probability that both marbles are green?
If two marbles are drawn at random from the jar and the first marble is not replaced before the second is drawn, what's the probability that both marbles are green?
What's the probability of you losing all your marbles?
Answer
1.
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4. If you continue hanging out with us Shmoopians...pretty good.
Example 2
Mr. and Mrs. Kappler bought ten books and plan to give one at random to each of their five kids. No one ever said they were attentive or considerate parents. Certainly not their children. If there's only one such way to distribute the books that will make every kid happy with their book, what's the probability that every kid will be happy with his or her book?
Answer
The number of ways to give 10 books to 5 kids is
10 × 9 × 8 × 7 × 6 = 30,240.
If only one such way will make every kid happy, the probability that every kid will be happy is .
Not very good odds. Especially when you consider that one of the books is titled, How to Turn That Frown Upside-Down: Dealing with Juvenile Depression.
Example 3
An ice cream parlor has 30 flavors but Su likes only half of them. It isn't because she's picky. This parlor features the flavors Charred Chocolate Chip, Swine Swirl, and Deuce de Leche. It doesn't actually do a lot of business.
If the scooper makes a three-scoop ice cream cone at random (using three different flavors),
(a) What is the probability Su will like all three flavors?
(b) What is the probability Su will like at least one flavor?
Answer
(a) The probability Su likes all three flavors is the probability that all three scoops were chosen from the 15 Su likes.
(b) The probability Su likes at least one flavor is
1 – (probability Su likes none of the flavors).
The probability Su likes none of the flavors is the probability that all 3 scoops were chosen from the 15 Su doesn't like. This probability is the same as the probability that Su likes all the flavors.
The probability that Su likes at least one flavor is
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Example 4
A jar has 10 vanilla candies, 4 chocolate candies, and 1 strawberry candy. Seems that shrimp candy company went under. Shocker. If 2 candies are drawn at random from the jar without replacement, what is the probability that both are strawberry?
Answer
Sadly, the probability is 0. There's only 1 strawberry candy in the jar, so it's impossible for 2 candies to be strawberry.
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