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Shelly's Sunday: A Probability Quiz

Follow our friend Shelly through a pleasant, somewhat probable Sunday afternoon. No theoretical math knowledge is required for this quiz--logical guesses will suffice--though you're certainly likely to do better if you have some. Good luck!

A multiple-choice quiz by avrandldr. Estimated time: 8 mins.

Author
avrandldr

Time
8 mins

Type
Multiple Choice

Quiz #
240,851

Updated
Dec 03 21

# Qns
10

Difficulty
Very Difficult

Avg Score
4 / 10

Plays
867

One at a Time - Single Page - Timed Game

Question 1 of 10

1. After church one Sunday, Shelly comes home and decides to make chocolate chip cookies. The bag she uses contains 200 chocolate chips, and she ends up making 20 cookies, which gives an average of 10 chips per cookie. She wants that first one she (randomly) chooses to be the perfect cookie--what is the liklihood that that first cookie will have at least 13 chocolate chips? Hint

About 20%

About 10%

About 5%

About 30%

NEXT>

Question 2 of 10

2. After some cookies, Shelly sits down on the sofa to watch the NASCAR race that she has been looking forward to all week. Her favorite drivers have always been the Labonte brothers, Terry and Bobby, and she's hoping that they both finish well in this race. If the race begins with 43 drivers, what is the (mathematical--pretending that no skill is involved) probability that both the Labonte brothers will finish in the top 10? Hint

About 10%

About 30%

About 20%

About 5%

NEXT>

Question 3 of 10

3. The Labonte brothers don't start too well in this particular race, but Shelly's interest is piqued at the first commercial break--she has three particular ads that she really enjoys. If there are 40 different commercials for the network to choose from in this programming segment, and the commercial break has 5 ads (no repeats), what is the probability that Shelly will see all three of her favorite ads sometime in the first commercial break? Hint

Between 5% and 10%

Greater than 25%

Between 10% and 25%

Less than 5%

NEXT>

Question 4 of 10

4. Disillusioned by a disappointing first advertisment, Shelly gives up on the ads, and decides to go order a pizza. She has a coupon for a two-topping medium pizza at half-price. When the order boy asks "Which toppings would you like?" Shelly, feeling frisky, instructs him to surprise her, and choose the toppings for her. Twenty minutes later, she realizes with horror that she has forgotten to tell him that she is allergic to onions. There are 22 different pizza toppings at the pizzeria (only 1 onion topping)--what is the liklihood that Shelly will be able to eat her pizza? Hint

Less than 10%

Greater than 60%

Between 10% and 40%

Between 40% and 60%

NEXT>

Question 5 of 10

5. The pizza turned out to have ham and green peppers on it--a good choice, Shelly thought. As she returned to watch the race, a commercial for the local Pick 4 lottery (in which one selects 4 numbers from 0 to 9 independently, hoping to match the lottery's 4 randomly chosen numbers--repeated numbers are possible) came on, stating that if someone were to get 3 of the 4 numbers correct, then he or she would receive 5 free lottery tickets. "I wonder what the chances are of that happening," Shelly wondered. What are they? Hint

Between 5% and 10%

Less than 5%

Between 10% and 15%

Greater than 15%

NEXT>

Question 6 of 10

6. The Labonte brothers finished a disappointing 16th and 34th in the race. Shelly got up, thinking that it was time for some exercise after an afternoon of pizza and cookies. As she left to go running, she noticed that someone had run over the stop sign near her house again. On her jog, she counted the other signs in her neighborhood--5 stop signs and 21 others. "I figure stop signs, being at intersections, are twice as likely to get hit as other signs," thought Shelly. If her counting and thinking is correct, what is the probability that the next sign in her neighborhood that gets run over will be a stop sign? Hint

Less than 10%

Between 20% and 30%

Between 10% and 20%

Greater than 30%

NEXT>

Question 7 of 10

7. As Shelly is stretching to cool down from her run, she notices something unusual--three of the doors across the street from her are painted blue. "How odd," Shelly thinks, "I wonder why I never noticed that before? That seems unlikely." If 10% of all homes have blue doors, and there are 15 townhouses across from Shelly's house, what is the probability that (exactly) 3 houses will have blue doors? Hint

Between 10% and 20%

Between 5% and 10%

Less than 5%

Greater than 20%

NEXT>

Question 8 of 10

8. After showering off, Shelly notices the cookies that she made once more. Specifically, she notices one cookie that appears to have no chocolate chips. Upon further inspection, the cookie proves to have a couple chips in it, but that leads Shelly to wonder whether it's possible by pure chance to end up with a cookie with no chocolate chips at all (provided that she mixed the batter thoroughly). Is it? Hint

No--it's impossible to get 0 chips if the distribution is truly random.

Yes, but it's always prohibitively unlikely.

Yes; in fact, getting 0 chips has a static probability of 0.1%.

Yes; the liklihood depends on the average number of chips per cookie.

NEXT>

Question 9 of 10

9. Shelly decides to call it an early night, and to just do the laundry and turn in. Pulling her things away from the dryer, she fails to notice that she has left 2 socks in the machine. If that load of laundry had 10 pairs of socks (20 socks altogether) in it, what is the probability that all the socks that Shelly has in her basket will match? Hint

About 10%

About 20%

About 15%

About 5%

NEXT>

Question 10 of 10

10. After washing up, Shelly is getting ready for bed, when the weatherman reports that there is a 40% chance of rain tomorrow. As she lies down, she tries to remember which of her friends is driving her carpool tomorrow--Dave, Ben, or Sheila. "Ben's late half the time," thinks Shelly, "and I don't want to be waiting around in the rain while he takes his time." She considers calling Sheila, but decides just to take her chances instead, and rolls over and goes to sleep. What is the probability that she will get caught in the rain as she feared? Hint

Greater than 30%

Between 10% and 20%

Less than 10%

Between 20% and 30%

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Quiz Answer Key and Fun Facts

Answer: About 20%

The exact probability is found most quickly using a Poisson distribution. A Poisson distribution has the formula P(n) = [e^(-x)*x^n]/n!, if x is the average number in a distribution (here, x = 10 chips) and n is the number you are interested in finding (for example, 13). You would begin by finding the liklihood of a cookie having 0 chips, then 1, then 2, and so on up to 12. You can then sum these to find that the liklihood that a cookie has 12 or less chips will be 79.15% (rounded).

Therefore, the probability that it has more chips than this will be 100% - 79.15% = 20.85%.

Answer: About 5%

Take Bobby first. Assuming the purely mathematical position, there are 10 chances out of 43 possibilities (23.26%) that Shelly could get the result she wants. There would then be 9 chances left out of 42 remaining possibilities (21.43%) for Terry to finish in the top 10. The probability of the two events happening simultaneously is their product, which rounds to about 4.98%.

Answer: Less than 5%

There are 37 unwanted ads and 3 wanted ones. The odds of picking a desired ad at the outset are 3/40. The odds of picking another one are then 2 out of the remaining 39. The probability of picking the third are then 1/38. The remaining two choices would have probabilities of 37/37 and 36/36 (100%) respectively.

The probability of all five events happening is the product of the individual events, which is just over 0.01%. This could happen in 10 different ways (1-2-3, 1-2-4, 1-2-5, 1-3-4, 1-3-5, 1-4-5, 2-3-4, 2-3-5, 2-4-5, and 3-4-5), so the total probability is just over 0.1%--not very likely.

Answer: Greater than 60%

Choosing a number of selected options out of a wide range of possibilites when order is unimportant is called a combination. The number of possibilities is found by the formula n!/[(n-r)!(r)!], where n is the number you are choosing from (in this problem, 22), and r is the number you will select (here, 2).

This gives 231 different 2-topping pizza combinations. There are 21 combinations that would contain onions--represented by onions paired with any of the other 21 options. So, the probability that her pizza has onions on it is 21/231; about 9.09%.

This gives a probability of 90.91% that her pizza will be just fine.

Answer: Less than 5%

There are four ways (YYYN, YYNY, YNYY, and NYYY) that you could get exactly three correct numbers. Each has the same probability--9 out of 1000, or 0.9%. (9/1000 comes from multiplying the individual probabilities of each of the four independent choices: 1/10 [right], 1/10 [right], 1/10 [right], and 9/10 [wrong]. You get the same result regardless of which order you multiply them.) As there are four chances, this results in a total probability of 3.6%.

Answer: Greater than 30%

By Shelly's count, stop signs represent 5/26 of the neighborhood signs. If you double the representation of stop signs in the 'sign pool,' then you arrive at a 10/31 chance (just as if there were 5 more stop signs in the neighborhood). This rounds to about 32.26%.

Answer: Between 10% and 20%

A problem such as this is most quickly solved using the Binomial Probability Formula, which incorporates the combination formula used earlier. It states that the probability of x successes in n trials = [Combination of n items, choosing x] * (probability of success)^x * (probability of failure^(n-x)), where x is the number of 'successes' you are looking for, given n trials. So here, you would find the combination of 15 items, choosing 3 (455--same combination formula as above), times the probability of success (0.10) to the 3rd power, times the probability of failure (0.90) to the power of the remaining trials (12).

This gives a probability of about 12.85% for having 3 blue doors across the street.

Answer: Yes; the liklihood depends on the average number of chips per cookie.

Remember the formula [e^(-x)*x^n]/n! from problem #1? Well, if n--the number you are interested in--is 0, then the formula simplifies completely to e^(-x). X represented the average number of chips per cookie, so the formula reduces to being completely dependent upon this factor. (By the way, the probability of having 0 chips in our example is .0000454, or about 1 in 22000.)

Answer: About 5%

All of Shelly's socks will match if and only if the pair left in the dryer is an exact match. Therefore, it doesn't matter what type of sock the first one we see is; the second one just has to match it. There is a 1 out of 19 chance that this will happen, or roughly 5.26%.

Answer: Less than 10%

The probability of rain given is 4/10, the probability of Ben driving at all is 1/3, and the probability of his being late is given at 1/2. The liklihood of all of these events happening together is their product (2/30), which rounds to 6.67%.

Source: Author avrandldr

This quiz was reviewed by FunTrivia editor crisw before going online.
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