Chapter 13.6, Problem 28STP

i.

To determine

The probability that the marble Casey will pick is white

Answer to Problem 28STP

The probability that the marble Casey will pick is white is $\frac{1}{5}$

Explanation of Solution

Given:

Casey has a bag which contains $3$ White, $8$ Red, $2$ blue, $2$ marbles. She repeats the experiment $250$ times.

Concept Used:

Calculation:

As per the given problem

First express the problem in the fraction form,

Now, to find the number of white marbles is given as,

  $P\left(white\right)=\frac{Frequencyofwhitemarbles}{Totalnoofmarbles}$

Substitute all the values in the above equation,

  $=\frac{3}{3+8+2+2}$

  $P\left(white\right)=\frac{3}{15}$

  $=\frac{1}{5}$

  $P\left(white\right)=\frac{1}{5}$

Percentage Form:

Now to convert the fraction into percentage multiply the no of white marbles by $100$ and add % at the end of number.

  $=\left(\frac{1}{5}\right)\times 100\%$

  $=\left(\frac{100}{5}\right)\%$

  = $20\%$

Conclusion:

The probability that the marble Casey will pick is white is $\frac{1}{5}$ .

ii.

To determine

The number of times out of $250$ Casey will pick a white marble.

Answer to Problem 28STP

The number of times out of $250$ Casey will pick a white marble is $50$ .ss

Explanation of Solution

Given:

Casey has a bag which contains $3$ White, $8$ Red, $2$ blue, $2$ marbles. She repeats the experiment $250$ times.

Concept Used:

Calculation:

The number of times Casey will pick the white marbles is given by,

Probability of white marbles $\times 100$

Probability of white marbles= $\frac{1}{5}$

Number of white marbles = $\frac{1}{5}$ $\times 100$

Number of white marbles $=50$

Hence, number of times out of $250$ Casey will pick a white marble is $50$