Random variables and binomial distributions

Front

What does the p stand for in the binomial probability formula?

Back

Probability of Successes

Front

Is this a binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Put the card back in the deck, shuffle again. Repeat the process 50 times. Let X = the number of aces you observe.

Back

Yes

Front

Find the probability for at least 4 questions correct on a 5 question true-false quiz.

Back

0.1875

Front

Is this a binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Do not replace the card. Repeat the process 5 times. Let X = the card you observe.

Back

No, there are more than 2 outcomes.

Front

The American Red Cross says that about 11% of the U.S. population has Type B blood. What is the probability that at least 2 of the first 10 blood donors has Type B blood?

Back

0.303

Front

Define a random variable.

Back

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

Front

What are the two types of random variables?

Back

Discrete and Continuous.

Front

What is a binomial distribution?

Back

A binomial distribution is the probability distribution of a binomial random variable, which counts the number of successes in a fixed number of independent Bernoulli trials.

Front

What are the parameters of a binomial distribution?

Back

The number of trials (n) and the probability of success (p).

Front

What is the formula for the binomial probability?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where k is the number of successes.