Question

franco has a hat with 9 blue marbles, 4 yellow marbles, and 12 green marbles. he designs a binomial experiment by drawing a marble from the hat, recording whether the marble is green, and then laying the marble aside. he then repeats the process seven times. which statement must be true?

the experiment is not a binomial experiment because there is not a fixed number of drawings.

the experiment is not a binomial experiment because the probability of choosing a green marble is the same for each drawing.

the experiment is not a binomial experiment because the probability of choosing a green marble is not the same for each drawing.

the experiment is not a binomial experiment because there are only two possible outcomes for each drawing.

Explanation:

To determine why the experiment is not binomial, recall binomial experiment requirements: fixed number of trials, independent trials (constant probability of success), two outcomes. Here, marbles are laid aside (without replacement), so the total number of marbles changes each time, altering the probability of choosing green. Thus, the probability isn’t constant for each drawing.

• First option: The process is repeated seven times (fixed trials) – false.
• Second option: Probability isn’t same (due to no replacement) – false.
• Third option: Correct, as no replacement changes probability each time.
• Fourth option: Two outcomes (green or not green) is a binomial requirement – false.

Answer:

The experiment is not a binomial experiment because the probability of choosing a green marble is not the same for each drawing.