Binomial Probability Practice Sheet

A fair coin is flipped 4 times. What is n, and what is p for landing on heads?

n = 4 trials; p = 0.5 (or 1/2).

Calculate the binomial coefficient 6 choose 2.

6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15.

A fair 6-sided die is rolled 5 times. What is the probability of rolling no sixes at all?

(5 choose 0) * (1/6)^0 * (5/6)^5 = 1 * 1 * (3125 / 7776) = 3125/7776, or approximately 0.4019 (40.19%).

A multiple-choice quiz has 4 questions, each with 5 answer choices. If you guess randomly on all 4, what is the probability of getting exactly 2 correct?

(4 choose 2) * (0.2)^2 * (0.8)^2 = 6 * 0.04 * 0.64 = 0.1536 (15.36%).

A machine produces parts that are defective 10% of the time. If a batch of 6 parts is inspected, what is the probability of finding exactly 1 defective part?

(6 choose 1) * (0.1)^1 * (0.9)^5 = 6 * 0.1 * 0.59049 = 0.354294, or approximately 0.3543 (35.43%).

Using the same machine from item 5 (defect rate 10%, sample of 6), calculate the probability of finding at least 1 defective part using the complement rule.

P(at least 1) = 1 - P(0) = 1 - [(6 choose 0) * (0.1)^0 * (0.9)^6] = 1 - 0.531441 = 0.468559, or approximately 0.4686 (46.86%).