Question

the chips shown are placed in a bag and drawn at random, one by one, without replacement. what is the probability that the first two chips drawn are both yellow? the probability is (simplify your answer.)

Explanation:

Step1: Count total and yellow chips

There are 12 chips in total and 3 yellow chips.

Step2: Calculate first - draw probability

The probability of drawing a yellow chip on the first draw is $\frac{3}{12}$.

Step3: Calculate second - draw probability

After drawing one yellow chip on the first draw, there are 2 yellow chips left and 11 chips in total. So the probability of drawing a yellow chip on the second draw is $\frac{2}{11}$.

Step4: Calculate combined probability

By the multiplication rule for independent events (in the context of non - replacement), the probability that the first two chips drawn are both yellow is $\frac{3}{12}\times\frac{2}{11}=\frac{6}{132}=\frac{1}{22}$.

Answer:

$\frac{1}{22}$