question_answer

100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has failed in both the examinations?

A)  \[\frac{1}{5}\] 

B)  \[\frac{1}{7}\]

C)  \[\frac{5}{7}\]                         

D)  \[\frac{5}{6}\]

Correct Answer: A

Solution :

(a): Let ?U? be universal set; U = 100 students no. of failed students \[=n\left( U \right)-n\left( A\cup B \right)=100-80=20\] From the figure it, is evident that 80 students passed at least 1 exam. Thus, 20 failed both and the required probability is 20/100=1/5.