Chapter 13, Problem 11STP

To determine

The probability of two marbles are chosen is to be estimated.

Answer to Problem 11STP

The probability of two marbles are chosen is $\frac{1}{19}$

Explanation of Solution

Given:

  $\begin{array}{l}{M}_b=7\\ M_r=5\\ M_g=8\end{array}$

Concept Used:

Probability of an event is calculated as:

  $P=\frac{n\left(E\right)}{n\left(S\right)}$

Where,

The probability of an event: $P$

The number of favourable outcomes: $n\left(E\right)$

The total number of events in the sample space: $n\left(S\right)$

Calculation:

The probability of getting two red marbles in the fraction form is calculated as:

The probability of the first marbleis red $P_1$ is ratio of number of red marbles and total number of marbles.

  $\begin{array}{l}{P}_1=\frac{M_r}{M_b+M_r+M_g}\\ P_1=\frac{5}{7+5+8}\\ P_1=\frac{5}{20}\\ P_1=\frac{1}{4}\end{array}$

The probability of the second marble is red $P_2$ is ratio of number of red marbles after removal of one white marble and total number of marbles.

  $\begin{array}{l}{P}_2=\frac{M_{r1}}{M_{b1}+M_{r1}+M_{g1}}\\ P_2=\frac{4}{7+4+8}\\ P_2=\frac{4}{19}\end{array}$

The probability of getting two red marbles is given by the following formula:

  $\begin{array}{l}P=P_1\times P_2\\ P=\frac{1}{4}\times \frac{4}{19}\\ P=\frac{1}{19}\end{array}$

Conclusion:

Hence,the probability of getting two red marbles is $P=\frac{1}{19}$ .