Chapter 10.1, Problem 16E

To determine

To calculate:

Marble for which experimental probability of drawing the marble the same as theoretical probability.

Answer to Problem 16E

The probability of the event that the black color for comes up in the drawing of balls is equal to the theoretical probability for the particular color coming up.

Explanation of Solution

Given information:

  

Calculation:

The question is related to probability of the favorable event.

Event is considered as drawing balls from the bag consisting of five balls of different colors each.

Now, the probability that a given face comes up at random at any throw is given by,

  $P$ (Any color coming up)

  $=\frac{1}{5}$

The outcomes as recording after drawing the balls for a consecutive $30$ times is shown in given table.

Now the probabilities for each colors are getting by,

  $P$ ( $1^{st}$ color coming up)

  $\begin{array}{l}=\frac{5}{30}\\ =\frac{1}{6}\end{array}$

  $P$ ( $2^{nd}$ color coming up)

  $\begin{array}{l}=\frac{6}{30}\\ =\frac{1}{25}\end{array}$

  $P$ ( $3^{rd}$ color coming up)

  $\begin{array}{l}=\frac{8}{30}\\ =\frac{4}{15}\end{array}$

  $P$ ( $4^{th}$ color coming up)

  $\begin{array}{l}=\frac{2}{30}\\ =\frac{1}{15}\end{array}$

  $P$ ( $5^{th}$ coming up)

  $\begin{array}{l}=\frac{9}{30}\\ =\frac{3}{10}\end{array}$

Hence, the probability of the event that the black color for comes up in the drawing of balls is equal to the theoretical probability for the particular color coming up.