Arun and Ved appeared for an interview for two vacancies. The probability of Arun’s selection is 1/4, and that of Ved’s rejection is 2/3. Find the probability that at least one of them will be selected.
Given : let A denote the event ‘Arun is selected’ and let B denote the event ‘ved is selected’.
Therefore , P(A) = 
and P(
) = 
P(B) = 
and P(
) = 
Also, A and B are independent .A and not B are independent, not A and B are independent.
To Find: The probability that atleast one of them will get selected.
Now,
P(atleast one of them getting selected) = P(selecting only Arun ) + P(selecting only ved) + P(selecting both)
= P(A and not B) +P (B and not A) +P (A and B)
= P( A 
) + P(B 
) + P( A 
B)
= P(A) 
P(
) + P(B) 
P(
) + P(A) 
P(B)
= 
+ 
)+ 
= 
+ 
+ 
= 
Therefore , The probability that atleast one of them will get selected is 