Understanding The Binomial Setting Quiz

1) Which of the following situations represents a binomial experiment?

Flipping a coin 10 times and counting the number of heads

Drawing 5 cards from a deck without replacement and counting the number of aces

Rolling a die until you get a six and counting the number of rolls

Selecting students from a class one by one without replacement until you find someone who plays sports

The experiment has a fixed number of independent trials, two outcomes, and constant probability.

Explanation

The experiment has a fixed number of independent trials, two outcomes, and constant probability.

2) In a binomial experiment, what must be true about the probability of success on each trial?

It must increase with each trial

It must decrease with each trial

It can vary randomly from trial to trial

It must remain constant for all trials

The probability of success must stay the same in every trial.

Explanation

The probability of success must stay the same in every trial.

3) A quality control inspector examines 15 light bulbs from a production line and records whether each bulb is defective or not. Which condition is necessary for this to be a binomial experiment?

Each bulb must have the same probability of being defective

The production line must produce exactly 15 bulbs per day

At least one bulb must be defective

The bulbs must be examined in a specific order

Each trial must have the same chance of success for it to be binomial.

Explanation

Each trial must have the same chance of success for it to be binomial.

4) How many possible outcomes must each trial have in a binomial experiment?

At least two

More than two

Any number of outcomes

Exactly two

Each trial has exactly two possible results — success or failure.

Explanation

Each trial has exactly two possible results — success or failure.

5) A student takes a 20-question true/false test by guessing on every question. Why is this a binomial experiment?

Because the student is guessing

Because there are 20 questions

Because true/false questions are always binomial

Because there are a fixed number of independent trials, each with two outcomes and constant probability

The test has fixed, independent trials, with two outcomes and constant probability.

Explanation

The test has fixed, independent trials, with two outcomes and constant probability.

6) Which of the following is NOT a requirement for a binomial experiment?

The trials must result in at least one success

Fixed number of trials

Each trial has only two possible outcomes

The probability of success remains constant

A binomial experiment does not require at least one success.

Explanation

A binomial experiment does not require at least one success.

7) A basketball player shoots free throws until she makes 10 baskets. Is this a binomial experiment?

Yes, because she is shooting free throws

Yes, because each shot is independent

No, because the number of trials is not fixed

No, because the probability changes with each shot

The number of trials is not fixed — she stops when she makes 10.

Explanation

The number of trials is not fixed — she stops when she makes 10.

8) In a binomial experiment with n trials, what does 'n' represent?

The number of successes

The fixed number of trials

The probability of success

The number of failures

“n” is the total number of trials in the experiment.

Explanation

“n” is the total number of trials in the experiment.

9) A bag contains 5 red marbles and 5 blue marbles. You draw one marble, record its color, replace it, and repeat this process 8 times. Why is this a binomial experiment?

Because the trials are independent with replacement, there are two outcomes, and the probability stays constant

Because there are equal numbers of red and blue marbles

Because you draw exactly 8 times

Because marbles are being drawn from a bag

Replacement keeps the trials independent and probability constant.

Explanation

Replacement keeps the trials independent and probability constant.

10) Which scenario violates the independence condition of a binomial experiment?

Flipping a coin 50 times

Rolling a die 100 times and recording if it shows a 6

Spinning a spinner 25 times

Drawing 10 cards from a deck without replacement

Without replacement, probabilities change, so trials aren’t independent.

Explanation

Without replacement, probabilities change, so trials aren’t independent.

11) Which scenario(s) represent a binomial experiment?

Scenario A only

Scenarios A and C only

Scenarios B and D only

Scenario C only

Both A and C have fixed trials, independence, two outcomes, and constant probability.

Explanation

Both A and C have fixed trials, independence, two outcomes, and constant probability.

12) Why is Scenario B NOT a binomial experiment?

Because there are more than two possible outcomes

Because the trials are not independent (sampling without replacement from a small population)

Because the number of trials is not fixed

Because the sample size is too small (less than 30)

Sampling without replacement means probabilities change each draw.

Explanation

Sampling without replacement means probabilities change each draw.

13) Why is Scenario D NOT a binomial experiment?

Because dice have more than two outcomes

Because the probability changes with each roll

Because the number of trials is not fixed in advance

Because the trials are not independent

The number of trials isn’t fixed — the player stops after rolling a 7.

Explanation

The number of trials isn’t fixed — the player stops after rolling a 7.

14) In Scenario A, what is considered a 'success' in the binomial experiment?

Selecting a bolt from the batch

Finding a defective bolt

Finding a non-defective bolt

Inspecting all 50 bolts

“Success” means the specific outcome being counted — a defective bolt.

Explanation

“Success” means the specific outcome being counted — a defective bolt.

15) A survey asks 100 randomly selected people whether they support a new policy (yes or no). Each person's response is independent. Is this a binomial experiment?

No, because people's opinions are never independent

No, because the probability of 'yes' is unknown

Yes, because all four conditions are met: fixed n, two outcomes, independent trials, and constant probability

Yes, but only if exactly 50 people say yes

There are two outcomes, independence, constant probability, and fixed trials.

Explanation

There are two outcomes, independence, constant probability, and fixed trials.

16) What distinguishes a binomial experiment from a geometric experiment?

Binomial experiments have two outcomes; geometric experiments have more

Binomial experiments have a fixed number of trials; geometric experiments continue until the first success

Binomial experiments have independent trials; geometric experiments do not

Binomial experiments have constant probability; geometric experiments have varying probability

Binomial has fixed trials; geometric continues until first success.

Explanation

Binomial has fixed trials; geometric continues until first success.

17) A student flips a coin 20 times. On the first 10 flips, the probability of heads is 0.5, but on the last 10 flips, the coin is weighted so the probability of heads is 0.7. Is this a binomial experiment?

Yes, because there are exactly two outcomes

Yes, because the number of trials is fixed

No, because the trials are not independent

No, because the probability of success is not constant across all trials

Probability of success changes, so it’s not binomial.

Explanation

Probability of success changes, so it’s not binomial.

18) In a binomial experiment, the trials must be:

Dependent on each other

Independent of each other

Conducted in a specific order

Successful at least 50% of the time

Each trial must be independent of the others.

Explanation

Each trial must be independent of the others.

19) A researcher tests 12 patients with a new drug and records whether each patient improves or does not improve. Assuming each patient's response is independent and the drug has the same effectiveness for all patients, this is a binomial experiment. What is n?

2

The number of patients who improve

12

The probability of improvement

“n” is the fixed number of trials, here 12 patients.

Explanation

“n” is the fixed number of trials, here 12 patients.