Binomial Probability

Front

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

Back

Probability of Failures.

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

What is the probability that Barry Bonds will get 6 hits in his next 10 at-bats if his batting average is .298?

Back

3.58%.

Front

If you flip a coin 20 times, what is the probability you would get exactly 10 heads?

Back

17.62%.

Front

What is the probability of getting at least 1 correct answer when randomly guessing on 5 multiple choice questions with 4 choices each?

Back

0.7627.

Front

Define a binomial experiment.

Back

A binomial experiment is a statistical experiment that has the following properties: a fixed number of trials, each trial has two possible outcomes (success or failure), the trials are independent, and the probability of success is constant for each trial.

Front

What is the formula for binomial probability?

Back

P(X = k) = (n choose k) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.

Front

What does the term 'n choose k' represent in the binomial probability formula?

Back

It represents the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).

Front

What is the probability of failure (q) if the probability of success (p) is 0.3?

Back

q = 1 - p = 1 - 0.3 = 0.7.

Front

In a binomial distribution, what does the mean (μ) represent?

Back

The mean (μ) represents the expected number of successes in n trials, calculated as μ = n * p.