Question

Which situation can be considered a binomial experiment?

A. Rolling a single number cube until you get a 3
B. Tossing a coin 10 times and recording the number of
times it lands on heads
C. Drawing one marble from a bag containing 10 red
and 7 blue marbles (replacing after each draw) until
you have drawn 4 blue marbles
D. Asking 15 students how tall they are and recording
their answers

Answer 1

The situation B, tossing a coin 10 times and recording the number of times it lands on heads, can be considered a binomial experiment as it meets all the required characteristics: fixed number of trials, two outcomes, constant probability, and independent trials.

Step-by-step explanation:

The situation that can be considered a binomial experiment is B. Tossing a coin 10 times and recording the number of times it lands on heads. This situation meets the required characteristics of a binomial experiment: a fixed number of trials (n=10), two possible outcomes (heads or tails), constant probability of success (probability of landing heads in each coin toss), and independence of trials (the result of one toss does not affect the others).

To elaborate, a binomial experiment must have the following characteristics:

• A fixed number of trials, n.
• Each trial must have only two possible outcomes (success or failure).
• The probability of success, p, is the same for each trial.
• The trials must be independent.

The other situations given in the question do not meet all of these criteria. For example, Joe conducting an experiment to flip a coin until he gets four heads in a row does not qualify because the number of trials is not fixed, as it could end after any number of flips.