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?
Answer
A
The experiment is not a binomial experiment because the probability of choosing a green marble is not the same for each drawing.
B
The experiment is not a binomial experiment because there is not a fixed number of drawings.
C
The experiment is not a binomial experiment because the probability of choosing a green marble is the same for each drawing.
D
The experiment is not a binomial experiment because there are only two possible outcomes for each drawing.
Explanation
A binomial experiment requires the probability of success to stay the same on every trial. Because Franco sets each marble aside, the total number of marbles and possibly the number of green marbles remaining change after each draw, so the probability of drawing green can change. There are seven fixed drawings and two recorded outcomes—green or not green—so choice A identifies the reason it is not binomial.
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