A box contains 50 marbles of three different colors: red, blue, and green. The theoretical… — JAMB UTME

A box contains $50$ marbles of three different colors: red, blue, and green. The theoretical probability of selecting a red marble at random is $\frac{3}{10}$ . In a probability experiment, a marble was drawn with replacement $250$ times, resulting in a red marble being drawn $85$ times. What is the positive difference between the experimental probability and the theoretical probability of selecting a red marble?

$\frac{1}{25}$ Answer
B
$\frac{7}{25}$
C
$\frac{1}{5}$
D
$\frac{17}{50}$

Answer

The positive difference between the experimental probability and the theoretical probability of selecting a red marble is

\frac{1}{25}

The experimental probability is the ratio of observed successful trials to total trials, which is

\frac{85}{250} = \frac{17}{50}

. The theoretical probability is given as

\frac{3}{10} = \frac{15}{50}

. Subtracting the theoretical probability from the experimental probability gives

\frac{17}{50} - \frac{15}{50} = \frac{2}{50} = \frac{1}{25}

Step-by-Step Solution

Calculate the experimental probability (relative frequency) of drawing a red marble.

\text{Experimental Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of trials}} = \frac{85}{250} = \frac{17}{50} = 0.34

Experimental probability is calculated using empirical trial outcomes.

Identify the given theoretical probability of drawing a red marble.

\text{Theoretical Probability} = \frac{3}{10} = \frac{15}{50} = 0.30

The theoretical probability is provided directly as

\frac{3}{10}

Compute the positive difference between experimental and theoretical probabilities.

\text{Difference} = \frac{17}{50} - \frac{15}{50} = \frac{2}{50} = \frac{1}{25} = 0.04

Subtracting theoretical probability from experimental probability gives the required positive difference.

Key Concept

Experimental vs Theoretical Probability

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