An unknown man is found murdered. The corpse has one gold plated tooth, right ear is pierced and a healed fracture of left hand thumb. A man with these characteristics is reported missing. what are the chances (probability) of the corpse being the missing man? (given the occurrence of the gold-plated teeth in the area, 1 in 5000, left hand thumb fractures 1 in 20000 and of right ear pierces 1 in 100).

Correct Answer: Option 4 ("1 in 100,00,000,000")

Step-by-Step Explanation:

To determine the probability (chances) that the corpse belongs to the missing person based on the given characteristics, we use the principle of independent probabilities in statistics and forensic identification.

Step 1: Identify the individual probabilities of each characteristic
From the given data, we have three independent characteristics:
1. Occurrence of a gold-plated tooth:

$P_1=\frac{1}{5000}$

2. Occurrence of a healed fracture of the left hand thumb:

$P_2=\frac{1}{20000}$

3. Occurrence of a pierced right ear:

$P_3=\frac{1}{100}$

Step 2: Calculate the combined probability of all three characteristics occurring together
Assuming these physical characteristics occur independently in the population, the combined probability ($P$) is calculated by multiplying the individual probabilities:

$P=P_1\times P_2\times P_3$

$P=\frac{1}{5000}\times \frac{1}{20000}\times \frac{1}{100}$

Step 3: Perform the multiplication
First, multiply the numbers in the denominator:

$5000\times 20000=\mathrm{100,000,000}$

Now, multiply by the third denominator:

$\mathrm{100,000,000}\times 100=\mathrm{10,000,000,000}$

Thus, the combined probability is:

$P=\frac{1}{\mathrm{10,000,000,000}}$

Using the Indian numbering system formatting, 10,000,000,000 is written as 100,00,000,000 (10 thousand crore).

Therefore, the chances of finding another individual with this exact combination of traits by random chance is 1 in 100,00,000,000.