Question

which scenario can be analyzed using binomial probability?
a. rolling a die to get a prime number
b. flipping a coin 10 times to count the number of heads
c. picking a marble from a bag, replacing it, and then picking a different color
d. drawing a red card from a deck without replacement

Explanation:

Binomial probability is used when there are a fixed number of independent trials, each with two possible outcomes (success or failure), and the probability of success is constant.

• Option a: Rolling a die once (not multiple times with a count of a specific outcome) doesn't fit the binomial model.
• Option b: Flipping a coin 10 times (fixed number of trials, two outcomes - head (success) or tail (failure), probability of head \(p = 0.5\) is constant) fits the binomial model.
• Option c: Picking a marble (even with replacement) and then picking a different color - the description is not about counting a specific number of successes in a fixed number of trials.
• Option d: Drawing a card without replacement - probability changes for each draw (not independent with constant probability).

Answer:

B. Flipping a coin 10 times to count the number of heads