Question

In an examination, out of 70 students some students pass in the examination and some students fail. If the probability of selecting a student who passed in the examination is 4 times the probability of selecting a student who failed in the examination, then the difference between the number of students who pass and the number of students who fail is

• A. 14
• B. 28
• C. 42
• D. 56

Answer 1

The correct option is C 42

Let the number of students who pass the examination be x.
Then, the number of students who fail the examination is (70 – x).
According to the question:
P(Passed in the examination) = 4 × P(failed in the examination)
$\Rightarrow \frac{\text{Number of students passed}}{\text{Total number of students}}=4\times \frac{\text{Number of students failed}}{\text{Total number of students}}$
$\Rightarrow \frac{x}{70}=\frac{4(70-x)}{70}$
$\Rightarrow x=280-4x$
$\Rightarrow 5x=280$
$\Rightarrow x=56$
Thus, the number of students who passed in the examination is 56 and the number of students who failed is (70 – 56) i.e., 14.
$\therefore \text{Difference}=56–14$
= 42
Hence, the correct answer is option (c).