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Model Paper 7 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 74 Marks
Question
Two students Ankit and Vinod appeared in an examination. The probability that Ankit will qualify the examination is $0.05$ and that Vinod will qualify is $0.10.$ The probability that both will qualify is $0.02.$
$i.$ Find the probability that atleast one of them will qualify the exam. $(1)$
$ii.$ Find the probability that atleast one of them will not qualify the exam. $(1)$
$iii.$ Find the probability that both Ankit and Vinod will not qualify the exam. $(2)$
OR
Find the probability that only one of them will qualify the exam. $(2)$
✓

Answer

$i.$ Let $E_1$ and $E_2$ denotes the events that Ankit and Vinod will respectively qualify the exam.
$P\left(E_1 \cup E_2\right)= P \left( E _1\right)+ P \left( E _2\right)- P \left( E _1 \cap E _2\right)$
$=0.05+0.10-0.02=0.13$
$iii.$ Let $E_1$ and $E_2$ denotes the events that Ankit and Vinod will respectively qualify the exam.
$=P\left(E_1^{\prime} \cap E_2^{\prime}\right)=P\left(\left(E_1 \cup E_2\right)^{\prime}\right)$
$=1- P \left(E_1 \cup E_2\right)=1-0.13=0.87$
OR
Let $E_1$ and $E_2$ denotes the events that Ankit and Vinod will respectively qualify the exam.
The probability that Vinod will not qualify the exam. 
Probability that only one of them will qualify the exam $= P \left(\left( E _1- E _2\right) \cup\left( E _2- E _1\right)\right)$
$=P\left(E_1-E_2\right)+P\left(E_2-E_1\right)$
$=P\left(E_1 \cup E_2\right)-P\left(E_1 \cap E_2\right)$
$=0.13-0.02=0.11$

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