Investigation 5: Finding the Binomial Distribution
Find the binomial distribution in Grade 10 probability. Identify binomial experiments, calculate P(X=k) using the formula, and interpret probabilities for repeated independent trials.
Key Concepts
New Concept There are four conditions that need to be met for a probability experiment to qualify as a binomial experiment.
What’s next Next, you’ll use these four conditions as a checklist to test whether different scenarios, like rolling dice or taking a test, are binomial experiments.
Common Questions
What are the conditions for a binomial experiment?
A binomial experiment has a fixed number of trials n, only two outcomes (success or failure) on each trial, constant probability p of success, and independent trials.
What is the binomial probability formula?
P(X = k) = C(n,k) × pᵏ × (1-p)^(n-k), where n is number of trials, k is number of successes, and p is probability of success on each trial.
How do you calculate P(exactly 3 heads in 5 flips)?
P(X=3) = C(5,3) × (0.5)³ × (0.5)² = 10 × 0.125 × 0.25 = 10 × 0.03125 = 0.3125. There is a 31.25% chance of exactly 3 heads in 5 fair coin flips.