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Probability and Binomial Distribution Quiz

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#1

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

1/6
Explanation

Each face has equal chance.

#2

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

1/2
Explanation

Half the cards are red.

#3

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

0.7
Explanation

Sum of all probabilities is 1.

#4

What is the expected value of a binomial distribution?

The average or mean value
Explanation

Center value of distribution.

#5

What is the complement rule in probability?

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

Probability of not A.

#6

What is the formula for the binomial probability distribution?

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

Calculates probability of k successes in n trials.

#7

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

3/8
Explanation

Use binomial distribution.

#8

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

Multiply the probabilities
Explanation

Events don't influence each other.

#9

What is the variance of a binomial distribution?

np(1-p)
Explanation

Measure of spread in distribution.

#10

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

Mean = np(1-p)
Explanation

Standard deviation formula.

#11

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

Number of trials
Explanation

Total attempts or experiments.

#12

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

Probability of success
Explanation

Chance of desired outcome.

#13

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

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

Probability of exact successes.

#14

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

0
Explanation

No overlap in outcomes.

#15

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

7/8
Explanation

Use complement probability.

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