A bag contains 5 red balls, 3 blue balls, and n green balls. The theoretical probability o… — JAMB UTME

A bag contains $5$ red balls, $3$ blue balls, and $n$ green balls. The theoretical probability of drawing a blue ball at random from the bag is $\frac{3}{20}$ . In a probability experiment, a ball is drawn at random from the bag and replaced $500$ times. If a green ball is observed $340$ times, calculate the absolute difference between the experimental probability and the theoretical probability of drawing a green ball.

Answer: 0.08

Answer

The absolute difference between the experimental probability and the theoretical probability of drawing a green ball is

0.08

(or

\frac{2}{25}

The theoretical probability of drawing a blue ball establishes that the bag contains

20

total balls, meaning there are

12

green balls. The theoretical probability of picking a green ball is therefore

\frac{12}{20} = 0.60

. The experimental probability is

\frac{340}{500} = 0.68

. Taking the positive difference gives

|0.68 - 0.60| = 0.08

Step-by-Step Solution

Find the total number of balls and the value of

n

n = 12

, Total balls =

20

The theoretical probability of picking a blue ball is

\frac{3}{8+n} = \frac{3}{20}

, giving

8 + n = 20

Find the theoretical probability of drawing a green ball

P(\text{Green})_{\text{theo}} = 0.60

There are

12

green balls out of

20

total balls, so

\frac{12}{20} = 0.60

Find the experimental probability of drawing a green ball

P(\text{Green})_{\text{exp}} = 0.68

500

trials, a green ball was observed

340

times, so

\frac{340}{500} = 0.68

Calculate the absolute difference

|0.68 - 0.60| = 0.08

Subtract the theoretical probability from the experimental probability and take the absolute value.

Key Concept

Comparison of theoretical probability based on outcome sample space and experimental probability based on observed trial relative frequencies.

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