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In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class has passed in only one subject is
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The correct answer is:
$\frac{13}{25}$
Consider the following events :
$A=A$ student is passed in Mathematics,
$B=$ A student is passed in Statistics.
Then, $P(A)=\frac{70}{125}, \quad P(B)=\frac{55}{125}$, $P(A \cap B)=\frac{30}{125}$.
Then Required probability is $P(A \cap \bar{B})+P(\bar{A} \cap B)=P(A)+P(B)-2 P(A \cap B)$
$=\frac{70}{125}+\frac{55}{125}-\frac{60}{125}=\frac{65}{125}=\frac{13}{25}$.
$A=A$ student is passed in Mathematics,
$B=$ A student is passed in Statistics.
Then, $P(A)=\frac{70}{125}, \quad P(B)=\frac{55}{125}$, $P(A \cap B)=\frac{30}{125}$.
Then Required probability is $P(A \cap \bar{B})+P(\bar{A} \cap B)=P(A)+P(B)-2 P(A \cap B)$
$=\frac{70}{125}+\frac{55}{125}-\frac{60}{125}=\frac{65}{125}=\frac{13}{25}$.
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