Two students Anil and Ashima appeared in an examination. probability that Anil will qualify examinat

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14.Probability

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Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10 .$ The probability that both will qualify the examination is $0.02 .$ Find the probability that Atleast one of them will not qualify the examination.

A

$0.98$

B

$0.98$

C

$0.98$

D

$0.98$

Solution

Let $E$ and $F$ denote the events that Anil and Ashima will qualify the examination, respectively. Given that

$P(E)=0.05$, $P(F)=0.10$ and $P(E \cap F)=0.02$

Then

$P$ (atleast one of them will not qualify)

$=1- P$ (both of them will qualify)

$=1-0.02=0.98$

Standard 11

Mathematics

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(IIT-1999)