Question:
A student is selected at random from a group of dropout students.
What is the probability that the student will not qualify the
examination ?
A student is selected at random from a group of dropout students.
What is the probability that the student will not qualify the
examination ?
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Read carefully: "selected from a group of dropout students" means the condition is already fixed, so it's a simple subtraction from 1.
Updated On: Sep 10, 2026
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Solution and Explanation
Concept:
• If \( P(A) \) is the probability of an event happening, then \( 1 - P(A) \) is the probability of it not happening.
Step 1: Identify the conditional probability of qualifying
Let \( A \) be the event that a student qualifies the examination.
The problem states that of the dropouts (\( E_1 \)), 5% qualify:
\[ P(A|E_1) = 5\% = 0.05 \]
Step 2: Find the probability of not qualifying
We need to find \( P(\bar{A}|E_1) \):
\[ P(\bar{A}|E_1) = 1 - P(A|E_1) \] \[ P(\bar{A}|E_1) = 1 - 0.05 = 0.95 \] The probability is 0.95.
• If \( P(A) \) is the probability of an event happening, then \( 1 - P(A) \) is the probability of it not happening.
Step 1: Identify the conditional probability of qualifying
Let \( A \) be the event that a student qualifies the examination.
The problem states that of the dropouts (\( E_1 \)), 5% qualify:
\[ P(A|E_1) = 5\% = 0.05 \]
Step 2: Find the probability of not qualifying
We need to find \( P(\bar{A}|E_1) \):
\[ P(\bar{A}|E_1) = 1 - P(A|E_1) \] \[ P(\bar{A}|E_1) = 1 - 0.05 = 0.95 \] The probability is 0.95.
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