A box contains 30 tickets numbered 1 to 30. In a probability experiment, a ticket is drawn… — JAMB UTME

A box contains $30$ tickets numbered $1$ to $30$ . In a probability experiment, a ticket is drawn at random from the box and its number recorded before being replaced. This trial is performed $150$ times, and a ticket with a number that is a multiple of $4$ is recorded $45$ times. What is the absolute difference between the experimental probability and the theoretical probability of selecting a ticket bearing a multiple of $4$ ?

$\frac{1}{15}$ Answer
B
$\frac{3}{10}$
C
$\frac{7}{30}$
D
$\frac{8}{15}$

Answer

The absolute difference between the experimental probability and the theoretical probability is

\frac{1}{15}

The theoretical probability of drawing a multiple of 4 is

\frac{7}{30}

since there are 7 favorable tickets (

4, 8, 12, 16, 20, 24, 28

) out of 30 total tickets. The experimental probability from 150 draws is

\frac{45}{150} = \frac{9}{30}

. Taking the absolute difference gives

\frac{9}{30} - \frac{7}{30} = \frac{2}{30} = \frac{1}{15}

Step-by-Step Solution

Determine the theoretical probability

Theoretical probability

P(T) = \frac{7}{30}

The multiples of

4

between

1

and

30

are

4, 8, 12, 16, 20, 24, 28

, giving

7

favorable outcomes out of

30

possible outcomes.

Determine the experimental probability

Experimental probability

P(E) = \frac{45}{150} = \frac{3}{10}

The event occurred

45

times out of

150

experimental trials.

Calculate the absolute difference between

P(E)

and

P(T)

|P(E) - P(T)| = |\frac{9}{30} - \frac{7}{30}| = \frac{2}{30} = \frac{1}{15}

Express both fractions with a common denominator of

30

and subtract the smaller probability from the larger.

Key Concept

Experimental probability is calculated from trial data (favorable trials divided by total trials), whereas theoretical probability is calculated from expected sample space outcomes (favorable outcomes divided by total sample space size).

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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