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 four chips drawn are all yellow? the probability is (simplify your answer.)

Explanation:

Step1: Count total chips

There are 15 chips in total.

Step2: Calculate first - draw probability

The probability that the first chip drawn is yellow is $\frac{4}{15}$ since there are 4 yellow chips out of 15.

Step3: Calculate second - draw probability

After drawing one yellow chip, there are 3 yellow chips left and 14 chips in total. So the probability that the second chip drawn is yellow is $\frac{3}{14}$.

Step4: Calculate third - draw probability

After drawing two yellow chips, there are 2 yellow chips left and 13 chips in total. So the probability that the third chip drawn is yellow is $\frac{2}{13}$.

Step5: Calculate fourth - draw probability

After drawing three yellow chips, there is 1 yellow chip left and 12 chips in total. So the probability that the fourth chip drawn is yellow is $\frac{1}{12}$.

Step6: Calculate combined probability

Since these are independent - like events (in the sense of sequential non - replacement draws), we multiply the probabilities. The probability that the first four chips drawn are all yellow is $\frac{4}{15}\times\frac{3}{14}\times\frac{2}{13}\times\frac{1}{12}=\frac{24}{32760}=\frac{1}{1365}$.

Answer:

$\frac{1}{1365}$