Understanding Road Accident Data Analysis

The question asks us to determine the ratio of the likelihood of a person escaping uninjured in a road accident to the likelihood of dying by Fire. We are provided with data from two tables analysing 10,000 road accidents involving an average of 3 people per accident in Delhi during 2020.

First, let's understand the total number of people involved in these accidents:

• Total number of accidents = 10,000
• Average people per accident = 3
• Total number of people involved = \(10,000 \times 3 = 30,000\)

Table I provides the analysis of severity for these people:

Table II provides an analysis of the causes of fatalities. Note that these percentages are out of the total fatalities, not out of the total people involved.

Calculating Likelihood of Escaping Uninjured

From Table I, the percentage of people who escaped uninjured is 47%. This percentage is based on the total number of people involved (30,000).

The likelihood (or probability) of a randomly selected person involved in an accident escaping uninjured is the percentage of uninjured people divided by 100.

Likelihood of escaping uninjured = \(\frac{\text{Percentage Uninjured}}{100} = \frac{47}{100} = 0.47\)

Calculating Likelihood of Dying by Fire

To find the likelihood of dying by Fire, we need to combine information from both tables.

From Table I, the percentage of people who suffered fatalities is 19% of the total people involved.

From Table II, the percentage of fatalities caused by Fire is 3% of the total fatalities.

So, the percentage of total people involved who died by Fire is 3% of the 19% fatalities.

Percentage of people dying by Fire = (Percentage of Fatalities) \(\times\) (Percentage of Fire Casualty out of Fatalities)

Percentage of people dying by Fire = \(19\% \times 3\% = \frac{19}{100} \times \frac{3}{100}\)

Percentage of people dying by Fire = \(0.19 \times 0.03 = 0.0057\)

The likelihood (or probability) of a randomly selected person involved in an accident dying by Fire is this percentage divided by 100.

Likelihood of dying by Fire = \(\frac{0.0057}{1} = 0.0057\)

Determining the Ratio P

The question states that the likelihood of escaping uninjured is P times that of dying by Fire.

Likelihood of escaping uninjured = P \(\times\) Likelihood of dying by Fire

Rearranging the formula to find P:

\(P = \frac{\text{Likelihood of escaping uninjured}}{\text{Likelihood of dying by Fire}}\)

Substitute the calculated likelihood values:

\(P = \frac{0.47}{0.0057}\)

Now, let's calculate the value of P:

\(P \approx 82.456\)

The question asks for the approximate value of P.

Comparing this value to the given options:

• 12
• 82
• 200
• 15

The value 82.456 is closest to 82.

Thus, approximately P will be equal to 82.

Revision Table: Road Accident Likelihood

Additional Information: Probability Concepts in Data Analysis

In this problem, we used concepts of probability based on percentages derived from statistical data. Here's a brief explanation:

• Probability: A measure of the likelihood of an event occurring. It is usually expressed as a number between 0 and 1, or as a percentage between 0% and 100%.
• Calculating Probability from Data: If you have data on a population, the probability of a specific outcome can be estimated as the number of times that outcome occurred divided by the total number of observations (in this case, total people involved). For percentages, it's simply Percentage / 100.
• Conditional Probability: Table II presents a form of conditional probability. It gives the probability of a specific cause *given* that a fatality occurred. For example, P(Dying by Fire | Fatality) = 3%.
• Joint Probability: To find the overall probability of dying by Fire (i.e., P(Dying by Fire)), we need to find the probability of the intersection of two events: being a fatality AND the cause being fire. This is calculated using the formula: P(A and B) = P(B | A) * P(A). In our case, A is 'being a fatality' and B is 'dying by fire'. So, P(Dying by Fire) = P(Dying by Fire | Fatality) * P(Fatality). We have P(Fatality) = 19% or 0.19, and P(Dying by Fire | Fatality) = 3% or 0.03. Thus, P(Dying by Fire) = \(0.03 \times 0.19 = 0.0057\). This confirms our calculation.

Understanding how to work with percentages and conditional probabilities is crucial for interpreting data presented in tables like these, especially in accident analysis and risk assessment.