Chapter 13.10, Problem 20PPS

To determine

The probability ofeach outcome of the marbles.

A blue marble, a yellow marble and then a red marble.

Answer to Problem 20PPS

The probability ofa blue marble, a yellow marble and then a red marbleis= $\frac{3}{364}$

Explanation of Solution

Given:

Blue: $5$

Red: $3$

Green: $4$

Yellow: $2$

Total Marbles: $5+3+4+2=14$

Calculation:

Fraction Form:

Calculate the probability of the blue, yellow and red marble is as follows.

First takethe number of blue marblesand then get total number of marbles.

P (First marble is blue) = $\frac{5}{14}$

Now remove the $1$ marble from blue marbles, the probability is,

P (Second marble is blue) = $\frac{2}{13}$

Now take the number red marbles after removed the $1$ yellow marbles,

P (Third marble is red) = $\frac{3}{12}$

P (blue then yellow and then red) = P (First) * P (Second)*P(Third)

  $\begin{array}{l}=\frac{5}{14}\times \frac{2}{13}\times \frac{1}{4}\\ =\left(\frac{\mathrm{5.2.1}}{\mathrm{14.13.4}}\right)\\ =\frac{10}{728}\\ =\frac{5}{364}\end{array}$

Conclusion:

Hence, P (blue then yellow and then red marbles)= $\frac{5}{364}$