Question:
A survey was conducted to find out the success rate of students who qualified the entrance examination by dropping a year after class XII.
As per the data collected, 40% students appearing in the examination were dropouts and the remaining students were regular students of class XII.
Of the dropouts, 5% qualify the examination while 10% of the regular students qualify the examination.
Based on the above information, answer the following questions. (i). Find the probability that a student selected at random is a regular student.
A survey was conducted to find out the success rate of students who qualified the entrance examination by dropping a year after class XII.
As per the data collected, 40% students appearing in the examination were dropouts and the remaining students were regular students of class XII.
Of the dropouts, 5% qualify the examination while 10% of the regular students qualify the examination.
Based on the above information, answer the following questions. (i). Find the probability that a student selected at random is a regular student.
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Always identify the primary partitioning of the sample space before looking at conditional probabilities.
Updated On: Sep 11, 2026
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Solution and Explanation
Concept:
• The sum of probabilities of all mutually exclusive and exhaustive events is 1.
Step 1: Define the events
Let \( E_1 \) be the event that the student is a dropout.
Let \( E_2 \) be the event that the student is a regular student.
Step 2: Use given data to find probability
Given that 40% of the students are dropouts:
\[ P(E_1) = 40\% = 0.40 = \frac{40}{100} = \frac{2}{5} \]
Step 3: Calculate the probability of a regular student
Since a student is either a dropout or a regular student:
\[ P(E_2) = 1 - P(E_1) \] \[ P(E_2) = 1 - 0.40 = 0.60 = \frac{3}{5} \] The probability is 0.6.
• The sum of probabilities of all mutually exclusive and exhaustive events is 1.
Step 1: Define the events
Let \( E_1 \) be the event that the student is a dropout.
Let \( E_2 \) be the event that the student is a regular student.
Step 2: Use given data to find probability
Given that 40% of the students are dropouts:
\[ P(E_1) = 40\% = 0.40 = \frac{40}{100} = \frac{2}{5} \]
Step 3: Calculate the probability of a regular student
Since a student is either a dropout or a regular student:
\[ P(E_2) = 1 - P(E_1) \] \[ P(E_2) = 1 - 0.40 = 0.60 = \frac{3}{5} \] The probability is 0.6.
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