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 there is not a fixed number of drawings.
B
The experiment is not a binomial experiment because the probability of choosing a green marble is the same for each drawing.
C
The experiment is not a binomial experiment because the probability of choosing a green marble is not 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 a fixed number of trials, two outcomes per trial, and the same probability of success on every trial. There are seven drawings and two outcomes (green or not green), but Franco lays each marble aside, so the probability of drawing green changes after each draw. Therefore, it is not binomial because the probability is not the same for each drawing.
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