Probability and Binomial Distribution Quiz

Test your knowledge on probability, binomial distribution, expected value, variance, and more with these 15 questions!

Practice Learn Test

What is the probability of rolling a 4 on a fair six-sided die?

1/6

1/8

1/4

1/2

In a deck of playing cards, what is the probability of drawing a red card?

1/2

1/3

1/4

1/5

If the probability of an event A is 0.3, what is the probability of the complement of A?

0.3

0.5

0.7

0.9

What is the expected value of a binomial distribution?

The most likely outcome

The average or mean value

The highest possible value

The value with the highest probability

What is the complement rule in probability?

P(A and B) = P(A) + P(B)

P(A or B) = P(A) + P(B)

P(A') = 1 - P(A)

P(A') = P(A) / P(B)

What is the formula for the binomial probability distribution?

(n choose k) * p^k * (1-p)^(n-k)

n! / (k! * (n-k)!) * p^k * (1-p)^(n-k)

p^k * (1-p)^(n-k) / (n choose k)

(k! * (n-k)!) / n! * p^k * (1-p)^(n-k)

If a fair coin is tossed three times, what is the probability of getting exactly two heads?

1/8

3/8

1/2

5/8

If two events are independent, what is the probability of both events occurring?

Add the probabilities

Multiply the probabilities

Subtract the probabilities

Divide the probabilities

What is the variance of a binomial distribution?

npq

np(1-p)

n(1-p)

#10

What is the relationship between mean and standard deviation in a binomial distribution?

Mean = Standard Deviation

Mean > Standard Deviation

Mean < Standard Deviation

Mean = np(1-p)

#11

In a binomial distribution, what does 'n' represent?

Number of successes

Number of trials

Probability of success

Probability of failure

#12

In a binomial distribution, what does 'p' represent?

Number of successes

Number of trials

Probability of success

Probability of failure

#13

What is the probability mass function (PMF) of a binomial distribution?

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

P(X = k) = n! / (k! * (n-k)!) * p^k * (1-p)^(n-k)

P(X = k) = p^k * (1-p)^(n-k) / (n choose k)

P(X = k) = (k! * (n-k)!) / n! * p^k * (1-p)^(n-k)

#14

If events A and B are mutually exclusive, what is the probability of both events occurring?

Depends on the specific events

Cannot be determined

#15

What is the probability of getting at least one head when tossing a fair coin three times?

1/2

7/8

1/8

3/4