A fair spinner is divided into 8 equal sectors numbered 1 to 8. In an experiment, the spin… — JAMB UTME

A fair spinner is divided into $8$ equal sectors numbered $1$ to $8$ . In an experiment, the spinner is spun $120$ times, and it lands on a multiple of $3$ a total of $36$ times. What is the positive difference between the experimental probability and the theoretical probability of landing on a multiple of $3$ ?

$\frac{1}{20}$ Answer
B
$\frac{3}{10}$
C
$\frac{1}{4}$
D
$\frac{1}{10}$

Answer

The positive difference between the experimental probability and theoretical probability is

\frac{1}{20}

The correct option is

\frac{1}{20}

. The theoretical probability of hitting a multiple of

3

on an

8

-sector spinner is

\frac{2}{8} = \frac{1}{4}

. The experimental probability over

120

spins with

36

successes is

\frac{36}{120} = \frac{3}{10}

. Subtracting theoretical probability from experimental probability gives

\frac{3}{10} - \frac{1}{4} = \frac{6-5}{20} = \frac{1}{20}

Step-by-Step Solution

Calculate the theoretical probability of landing on a multiple of

3

The sample space is

\{1, 2, 3, 4, 5, 6, 7, 8\}

(total

8

outcomes). Multiples of

3

in this set are

\{3, 6\}

(

2

outcomes). Thus,

P(\text{Theoretical}) = \frac{2}{8} = \frac{1}{4}

Theoretical probability is the ratio of favorable outcomes to total possible outcomes in a fair trial.

Calculate the experimental probability (relative frequency) from the trial results.

P(\text{Experimental}) = \frac{36}{120} = \frac{3}{10}

Experimental probability is defined as the number of observed successful events divided by the total number of trials conducted.

Find the positive difference between the experimental and theoretical probabilities.

\text{Difference} = \frac{3}{10} - \frac{1}{4} = \frac{6}{20} - \frac{5}{20} = \frac{1}{20}

Subtracting the smaller theoretical probability from the larger experimental probability yields the positive difference.

Key Concept

Experimental versus Theoretical Probability

Estimated Time:1m 30s

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