Question

A box contains 8 red chips, 6 blue chips, and 12 white chips. Three chips are randomly drawn from the box and are not replaced.

Determine P(red, white, white).

Short answer

The required probability is $\frac{22}{325}$.

Step-by-step solution

Step 1. Define the meaning of probability.

The probability is a measure of the likelihood of an event to occur.

Step 2. Define the meaning of random event.

A random event is an event whose outcome is unpredictable.

Step 3. Determine the probability P(red, red, red).

Since, the three chips are randomly drawn from the box and are not replaced.

To determine the probability, choose one chip from red chips, one chip from white chips and one chip from white chips.

First chip: P(red)$=\frac{8}{26}$

Second chip: P (white)$=\frac{12}{25}$

Third chip: P (white)$=\frac{11}{24}$

P (red, white, white)$=\frac{8}{26}\times \frac{12}{25}\times \frac{11}{24}=\frac{22}{325}$

Therefore the required probability is $\frac{22}{325}$.