A fair six-sided die is rolled 150 times in a probability experiment. If the number 4 land… — JAMB UTME

A fair six-sided die is rolled $150$ times in a probability experiment. If the number $4$ lands face up $35$ times, what is the positive difference between the experimental probability and the theoretical probability of rolling a $4$ ?

$\frac{1}{15}$ Answer
B
$\frac{7}{30}$
C
$\frac{1}{6}$
D
$\frac{2}{5}$

Answer

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

\frac{1}{15}

The theoretical probability of getting a 4 on a fair die is

\frac{1}{6}

, which simplifies to

\frac{5}{30}

. The experimental probability from

35

successes out of

150

trials is

\frac{35}{150} = \frac{7}{30}

. Taking the positive difference yields

\frac{7}{30} - \frac{5}{30} = \frac{2}{30} = \frac{1}{15}

Step-by-Step Solution

Calculate the theoretical probability of rolling a 4 on a fair six-sided die

P(\text{theoretical}) = \frac{1}{6}

A fair six-sided die has 6 equally likely outcomes, and exactly one outcome is 4.

Calculate the experimental probability based on the experiment results

P(\text{experimental}) = \frac{35}{150} = \frac{7}{30}

Experimental probability is the ratio of successful trials (35) to the total number of trials (150).

Subtract the theoretical probability from the experimental probability to find the positive difference

\text{Difference} = \frac{7}{30} - \frac{1}{6} = \frac{7}{30} - \frac{5}{30} = \frac{2}{30} = \frac{1}{15}

Converting to a common denominator of 30 allows straightforward subtraction.

Key Concept

Comparing experimental probability (relative frequency from trials) to theoretical probability (expected frequency based on equally likely outcomes).

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