A box contains 10 pink rubber bands and 20 brown rubber bands. What is the probability of picking a pink rubber band, not replacing it, and then picking another pink rubber band? P(pink and then pink)

Answer 1

There are a few ways to approach this problem, but one common method is to use the multiplication rule of probability. This rule states that if two events are independent, meaning that the outcome of one does not affect the outcome of the other, then the probability of both events occurring is the product of their individual probabilities.

Using this rule, we can find the probability of picking a pink rubber band on the first draw as:

P(pink on first draw) = number of pink bands / total number of bands
P(pink on first draw) = 10 / 30
P(pink on first draw) = 1/3

Since we are not replacing the first rubber band, the total number of bands for the second draw will be one less than the original total. Therefore, the probability of picking another pink rubber band on the second draw, given that the first one was pink, is:

P(pink on second draw | first was pink) = number of remaining pink bands / remaining total bands
P(pink on second draw | first was pink) = 9 / 29

To find the probability of both events occurring, we multiply these probabilities together:

P(pink and then pink) = P(pink on first draw) * P(pink on second draw | first was pink)
P(pink and then pink) = (1/3) * (9/29)
P(pink and then pink) ≈ 0.103

Therefore, the probability of picking a pink rubber band, not replacing it, and then picking another pink rubber band is approximately 0.103, or about 10.3%.