Probability : In a class of 125 students 70 passed in Mathematics , 55 in Statistics and 30 in both. Then find the probability that a student selected at random from the class has passed in only one subject .
My approach :
Let n(M) = 70 ( students passed in mathematics) ; n(S) = 55 ( students passed in Statistics) ; n(M $\cap S) = 30.$
Therefore, probability of students passed in mathematics = $\frac{70}{125}; $
Probability of students passed in statistics = = $\frac{55}{125}; $
Using $$P(M \cup S) = P(M) + P(S) – P(M \cap S)$$
$$\Rightarrow P(M \cup S) = \frac{70}{125} + \frac{55}{125} – \frac{30}{125} = \frac{19}{25}$$
But the answer is wrong ; book answer is : $\frac{13}{25}$
Please correct where I am wrong.. thanks..
Best Answer
We need $$P(M\cap \bar S)+P(\bar M\cap S)$$
Now, $$P(M\cap \bar S)=P(M\cap(U-S))=P(M)-P(M\cap S)$$