Forty percent of the beads in a bag of more than 10 comma 000 beads are yellow. Suzy pulls out 10 beads, one at a time with replacement, and notes that eight of these beads are yellow. She says the next bead pulled out will not be yellow because a yellow bead has been pulled out too many times in a row. Is Suzy’s reasoning correct?
Answer
A
Yes, it is unlikely that she would pull out so many yellow beads, so the next bead cannot be yellow.
B
No, it is true that the probability of pulling a yellow bead is 0 point 4 0 , but Suzy should not expect that exactly 40 percent of such a small number of beads pulled will be yellow.
C
Yes, Suzy has correctly decided that more than 40 percent of the beads in this large bag are yellow.
D
No, if a yellow bead is pulled 8 out of 10 times, the bag of beads is unfairly weighted toward yellow.
Explanation
Because each bead is replaced, every pull has a 0.40 probability of being yellow, regardless of the previous pulls. Eight yellow beads in ten pulls is possible due to chance; Suzy should not expect a small sample to contain exactly 40% yellow beads. So she cannot conclude that the next bead will not be yellow.
AI-written and checked against the verified answer.