Probability Question 343
Question: 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
[EAMCET 1993]
Options:
A) $ \frac{13}{25} $
B) $ \frac{3}{25} $
C) $ \frac{17}{25} $
D) $ \frac{8}{25} $
Show Answer
Answer:
Correct Answer: A
Solution:
Consider the following events : $ A= $ A student is passed in Mathematics, $ B= $ A student is passed in Statistics. Then $ P(A)=\frac{70}{125}, $
$ P(B)=\frac{55}{125}, $
$ P(A\cap B)=\frac{30}{125}. $ Required probability is $ P(A\cap \bar{B})+P(\bar{A}\cap B) $
$ =P(A)+P(B)-2P(A\cap B) $
$ =\frac{70}{125}+\frac{55}{125}-\frac{60}{125}=\frac{65}{125}=\frac{13}{25}. $
BETA
