Question

Two students X and Y appeared in an examination. The probability that X will qualify the examination is $0.05$ and Y will qualify the examination is $0.10$. The probability that both will qualify the examination is $0.02$. What is the probability that only one of them will qualify the examination?

• A. $0.15$
• B. $0.14$
• C. $0.12$
• D. $0.11$

Answer 1

The correct option is D $0.11$

Two students X and Y appeared in an examination

Given that :

$P\left(X\right)=0.05$

$P\left(Y\right)=0.10$

then, $P(X\bigcap Y)=0.02$

P(only one of them will qualify the examination)

= $P(X\bigcap Y^{\prime })+P(X^{\prime }\bigcap Y)$

We Know That $P(A\bigcap B^{\prime })=P\left(A\right)-P(A\bigcap B)$

therefore,

= $P\left(X\right)-P(X\bigcap Y)+P\left(Y\right)-P(X\bigcap Y)$

= $0.05-0.02+0.10-0.02$

= $0.015-0.04$

= $0.11$

Hence the probability that only one of them will qualify the examination is $0.11$