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Probability — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSProbability3 Marks
Question
100 students appeared for two examination, 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has passed at least one examination.
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Answer

$\text{n}(\text{S})=100$
Let A be the event that students passed in first examination
$\therefore\text{p}(\text{A})=\frac{60}{100}$ [60 students were passed in first exam]
Let B be the event that students passed in second examination
$\therefore\text{p}(\text{B})=\frac{50}{100}$ [50 students were passed in second exam]
$\text{P}(\text{A}\cap\text{B})=\frac{30}{100}$ [$\because$ 30 students passed in both exam]
$\therefore\text{P}(\text{A}\cup\text{B})=\text{p}(\text{A})+\text{p}(\text{B})-\text{P}(\text{A}\cap\text{B})$
$=\frac{60}{100}+\frac{50}{100}-\frac{20}{100}=\frac{8}{100}$
$=\frac{4}{5}$

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