A cup on the teacher's desk contains 12 pens. There are 3 pens with blue ink and 9 pens with black ink. One student at a time selects a pen at random to sign the attendance sheet and then puts the pen back in the cup.
What is the probability that the first three students all randomly select a pen with blue ink?
First, we need to determine the total number of possible outcomes for the first three students selecting a pen. Since there are 12 pens in total, each student has 12 options to choose from.
The probability that the first student selects a pen with blue ink is 3/12, as there are 3 pens with blue ink out of 12 total pens.
The probability that the second student selects a pen with blue ink is also 3/12, as the pens are being replaced back into the cup after each selection.
Likewise, the probability that the third student selects a pen with blue ink is 3/12.
To find the probability of all three students selecting a pen with blue ink, we multiply the individual probabilities together:
(3/12) * (3/12) * (3/12) = 27/1728 = 1/64
Therefore, the probability that the first three students all randomly select a pen with blue ink is 1/64.