Question 1

A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads
On the next flip is
A) less than 50%, since "tails" is due to come up.
B) greater than 50%, since it appears that we are in a streak of "heads."
C) It cannot be determined.
D) 50%.

Accepted Answer

Each flip of a fair coin is an independent event, so the probability of getting heads on any single flip is always 50%, regardless of previous outcomes.

Question 2

BatCo, a company that sells batteries, claims that 99.5% of their batteries are in working order. How
Many would you expect to buy, on average, to find one that does not work?
A) 5
B) 995
C) 2000
D) 200
E) 100

Accepted Answer

D

Question 3

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to
the bike. 34% of the bikes sold have both features.
-Given that a randomly selected bike has a kickstand, what are the chances that it also has a water
Bottle holder?
A) 21%
B) 61.8%
C) 34%
D) 26%
E) 56.7%

Accepted Answer

The probability that a bike has both features is 34%. Given that a bike has a kickstand (55%), the probability it also has a water bottle holder is 34% / 55% = 61.8%.

Question 4

In a stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of
students eat breakfast and also floss their teeth.
-What is the probability that a student from this class eats breakfast or flosses?
A) 34%
B) 11%
C) 9%
D) 91%
E) 57%

Accepted Answer

The probability that a student eats breakfast or flosses is calculated using the formula P(A or B) = P(A) + P(B) - P(A and B). Here, P(A) = 57%, P(B) = 80%, and P(A and B) = 46%. So, P(A or B) = 57% + 80% - 46% = 91%.

Question 5

On a physical fitness test middle school boys are awarded one point for each push-up they can do,
And a point for each sit-up. National results showed that boys average 18 pushups with a standard
Deviation of 4 push-ups, and 34 sit-ups with standard deviation 11. The mean of their combined
(total) scores was therefore 18 + 34 = 52 points. What is the standard deviation of their combined
Scores?
A) 137
B) 11.7
C) 5.3
D) cannot be determined
E) 15

Accepted Answer

The answer of On a physical fitness test middle school...

Question 6

A friend of yours plans to toss a fair coin 200 times. You watch the first 40 tosses, noticing that she
Got only 16 heads. But then you get bored and leave. If the coin is fair, how many heads do you
Expect her to have when she has finished the 200 tosses?
A) 100
B) 116
C) 92
D) 96
E) 80

Accepted Answer

The answer of A friend of yours plans to toss...

Question 7

A supermarket claims that their checkout scanners correctly price 99.8% of the items sold. How
Many items would you expect to buy, on average, to find one that scans incorrectly?
A) 998
B) 500
C) 200
D) 99.8
E) 2

Accepted Answer

The answer of A supermarket claims that their checkout scanners...

Question 8

Political analysts estimate the probability that Candidate A will run for president in the next
Election is 45%, and the probability that Candidate B will run is 20%. If their political decisions are
Independent, then what is the probability that only Candidate A runs for president?
A) 36%
B) 45%
C) 25%
D) 11%
E) 9%

Accepted Answer

The probability that only Candidate A runs is the probability that A runs and B does not run. This is calculated as 0.45 * (1 - 0.20) = 0.45 * 0.80 = 0.36 or 36%.

Question 9

A survey of some AP* Stats students recorded gender and whether the student was left or
Right-handed. Results were summarized in a table like the one shown. If it turned out that
Handedness was independent of gender, how many of the AP* Stats students were lefty girls? 
A) 7
B) 4
C) 9
D) 10
E) cannot be determined

Accepted Answer

The answer of A survey of some AP* Stats students...

Question 10

According to the National Telecommunication and Information Administration, 50.5% of U.S.
Households had Internet access in 2001. What is the probability that four randomly selected U.S.
Households all had Internet access in 2001?
A) 12.6%
B) 93.5%
C) 49.5%
D) 6.5%
E) 50.5%

Accepted Answer

The answer of According to the National Telecommunication and Information...

Question 11

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to
the bike. 34% of the bikes sold have both features.
-What is the probability that a randomly selected bicycle will have a kickstand or a water bottle
Holder?
A) 81%
B) 34%
C) none of these
D) 56.7%
E) 61.8%

Accepted Answer

The probability of a bike having a kickstand or a water bottle holder is calculated using the formula P(A or B) = P(A) + P(B) - P(A and B). Here, P(A) = 0.60, P(B) = 0.55, and P(A and B) = 0.34. So, P(A or B) = 0.60 + 0.55 - 0.34 = 0.81 or 81%.

Question 12

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift. 
-If the restaurant is open for 8 hours each day, what are the mean and standard deviation for the total number of workers in a day, respectively? (assume that the each hour is independent)
A) 37.2, 2.24
B) 36, 3.14
C) 36, 8.88
D) none of these
E) 37.2, 6.34

Accepted Answer

The mean number of workers per hour is 4.65, so for 8 hours, the mean is 4.65 * 8 = 37.2. The standard deviation for one hour is 0.8, so for 8 independent hours, the standard deviation is sqrt(8) * 0.8 = 2.24.

Question 13

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to
the bike. 34% of the bikes sold have both features.
-We can tell that these two features are independent because…
A) These two features don't have anything to do with each other, so we know they're independent.
B) The probability of having a kickstand given that you have a water bottle (56.7%) is about equal to the probability of having a kickstand (55%).
C) The probability of having both features (34%) does not equal the probability of having neither feature (19%).
D) The probability of having both features is not zero; it is 34%.
E) The probability of having either feature (81%) doesn't equal the probability of having just one feature (60% and 55%).

Accepted Answer

The probability of having a kickstand given that you have a water bottle holder (56.7%) is approximately equal to the probability of having a kickstand (55%), indicating independence.

Question 14

Which of these random variables has a binomial model?
A) The number of girls a family has out of the three children they will have.
B) The number of books we select out of a pile of 9 books that are non-fiction.
C) none of these
D) The number of children a family has until they have two boys.
E) The number of times a free throw is shot until one shot is made.

Accepted Answer

The binomial model applies to situations with a fixed number of independent trials, each with two possible outcomes (success or failure). Option A fits this model as it involves a fixed number of trials (3 children) and two outcomes (girl or not a girl).

Question 15

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift. 
-If the workers are paid $10/hour, what is the expected long-term cost of a 1-hour shift?
A) $45
B) none of these
C) $180
D) $4.65
E) $46.50

Accepted Answer

The expected long-term cost of a 1-hour shift is the sum of the hourly wage and the expected cost of benefits. The hourly wage is $10, and the expected cost of benefits is $36.50 per hour. Therefore, the expected long-term cost of a 1-hour shift is $10 + $36.50 = $46.50.

Question 16

Which of these random variables has a geometric model?
A) The number of Democrats among a group of 20 randomly chosen adults.
B) The number of aces among the top 10 cards in a well-shuffled deck.
C) The number of cars inspected until we find three with bad mufflers.
D) The number of people we check until we find someone with green eyes.
E) The number of cards of each suit in a 10-card hand.

Accepted Answer

A geometric model is used for the number of trials until the first success in a series of independent Bernoulli trials, which matches option D.

Question 17

Five juniors and four seniors have applied for two open student council positions. School
Administrators have decided to pick the two new members randomly. What is the probability they
Are both juniors or both seniors?
A) 0.444
B) 0.395
C) 0.569
D) 0.506
E) 0.722

Accepted Answer

The probability of picking two juniors is (5/9) * (4/8) = 20/72. The probability of picking two seniors is (4/9) * (3/8) = 12/72. Adding these probabilities gives (20/72) + (12/72) = 32/72 = 0.444.

Question 18

The city council has 6 men and 3 women. If we randomly choose two of them to co-chair a
Committee, what is the probability these chairpersons are the same gender?
A) 5/9
B) 7/8
C) 4/9
D) 1/2
E) 5/8

Accepted Answer

The answer of The city council has 6 men and...

Question 19

In a large 2lb. bag of candies (the true fun size!) 15% of the candies are green. The chances of
Pulling out at least one green candy in three tries is… 
A) $1 - ( 0.85 ) ^ { 3 }$
B) $1 - ( 0.15 ) ^ { 3 }$
C) $( 0.85 ) ^ { 2 } ( 0.15 )$
D) none of these
E) $\left( \begin{array} { l } 3 \ 1 \end{array} \right) ( 0.15 ) ^ { 1 } ( 0.85 ) ^ { 2 }$

Accepted Answer

The probability of not pulling a green candy in one try is 0.85. The probability of not pulling a green candy in three tries is $ (0.85)^3 $. Therefore, the probability of pulling at least one green candy in three tries is $ 1 - (0.85)^3 $.

Question 20

If a 6-sided die is rolled 5 times and rolling a 2 is considered to be a success, what are the chances
Of rolling exactly three successes?
A) 16.67%
B) 33.33%
C) 32.15%
D) none of these
E) 0.32%

Accepted Answer

The probability of rolling a 2 on a 6-sided die is 1/6. Using the binomial probability formula for exactly 3 successes in 5 trials, the probability is calculated as: (5 choose 3) * (1/6)^3 * (5/6)^2 = 0.03215 or 3.215%, which is closest to 32.15% when rounded.

Quiz 4: Randomness and Probability

A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads On the next flip is

BatCo, a company that sells batteries, claims that 99.5% of their batteries are in working order. How Many would you expect to buy, on average, to find one that does not work?

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to the bike. 34% of the bikes sold have both features. -Given that a randomly selected bike has a kickstand, what are the chances that it also has a water Bottle holder?

In a stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of students eat breakfast and also floss their teeth. -What is the probability that a student from this class eats breakfast or flosses?

A friend of yours plans to toss a fair coin 200 times. You watch the first 40 tosses, noticing that she Got only 16 heads. But then you get bored and leave. If the coin is fair, how many heads do you Expect her to have when she has finished the 200 tosses?

A supermarket claims that their checkout scanners correctly price 99.8% of the items sold. How Many items would you expect to buy, on average, to find one that scans incorrectly?

Political analysts estimate the probability that Candidate A will run for president in the next Election is 45%, and the probability that Candidate B will run is 20%. If their political decisions are Independent, then what is the probability that only Candidate A runs for president?

A survey of some AP* Stats students recorded gender and whether the student was left or Right-handed. Results were summarized in a table like the one shown. If it turned out that Handedness was independent of gender, how many of the AP* Stats students were lefty girls?

According to the National Telecommunication and Information Administration, 50.5% of U.S. Households had Internet access in 2001. What is the probability that four randomly selected U.S. Households all had Internet access in 2001?

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to the bike. 34% of the bikes sold have both features. -What is the probability that a randomly selected bicycle will have a kickstand or a water bottle Holder?

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift. -If the restaurant is open for 8 hours each day, what are the mean and standard deviation for the total number of workers in a day, respectively? (assume that the each hour is independent)

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to the bike. 34% of the bikes sold have both features. -We can tell that these two features are independent because…

Which of these random variables has a binomial model?

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift. -If the workers are paid $10/hour, what is the expected long-term cost of a 1-hour shift?

Which of these random variables has a geometric model?

Five juniors and four seniors have applied for two open student council positions. School Administrators have decided to pick the two new members randomly. What is the probability they Are both juniors or both seniors?

The city council has 6 men and 3 women. If we randomly choose two of them to co-chair a Committee, what is the probability these chairpersons are the same gender?

In a large 2lb. bag of candies (the true fun size!) 15% of the candies are green. The chances of Pulling out at least one green candy in three tries is…

If a 6-sided die is rolled 5 times and rolling a 2 is considered to be a success, what are the chances Of rolling exactly three successes?