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Q 28/30

A poll was taken among 10,000 people working in Bangalore. The aim was to see what their annual salaries were.

\begin{tabular}{|l|c|}
\hline Annual Salary & Number of people \\
\hline Less than ₹ 40,000 & 200 \\
\hline ₹ 40,001 to ₹ 75,000 & 880 \\
\hline ₹ 75,001 to ₹ 150,000 & 1,080 \\
\hline ₹ 150,001 to ₹ 250,000 & 3,136 \\
\hline More than ₹ 250,000 & 4,704 \\
\hline
\end{tabular}

If you choose a person at random from this group, what is the probability that he or she earns more than ₹ 40,000 annually?



Answer :

GinnyAnswer
To determine the probability that a randomly selected person from this group earns more than ₹ 40000 annually, we can proceed with the following steps:

1. Identify the total number of people surveyed:
According to the poll data, the total number of people surveyed is 10,000.

2. Determine the number of people earning more than ₹ 40000 annually:
From the given data, individuals earning more than ₹ 40000 are distributed over three salary brackets:
- ₹ 40001 to ₹ 75000: 880 people
- ₹ 75001 to ₹ 150000: 1080 people
- ₹ 150001 to ₹ 250000: 3136 people
- More than ₹ 250000: 4704 people

By adding these numbers, the total number of people earning more than ₹ 40000 is:
[tex]\[ 880 + 1080 + 3136 + 4704 = 9800 \][/tex]

3. Calculate the probability:
The probability that a randomly selected person earns more than ₹ 40000 annually is the ratio of the number of people earning more than ₹ 40000 to the total number of people surveyed.

Thus, the probability [tex]\( P \)[/tex] is given by:
[tex]\[ P = \frac{\text{Number of people earning more than } ₹ 40000}{\text{Total number of people}} \][/tex]

Substituting the numbers, we get:
[tex]\[ P = \frac{9800}{10000} = 0.98 \][/tex]

Therefore, the probability that a randomly chosen person from this survey group earns more than ₹ 40000 annually is 0.98.

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