The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the lette...

The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname

What is the probability that the surname of a child picked at random from the class begins with either O or A?

Answer Details

There are a total of 40 children in the class. The probability of choosing a child with a surname beginning with O is 16/40, and the probability of choosing a child with a surname beginning with A is 9/40. However, we have to be careful not to double-count the surnames that begin with both O and A. Therefore, we need to subtract the probability of choosing a child with a surname beginning with both O and A, which is the intersection of the two events. The intersection is the number of surnames that begin with both O and A, which is zero in this case because it is not given that any surname starts with both O and A. So the probability of choosing a child with a surname beginning with either O or A is: P(O or A) = P(O) + P(A) - P(O and A) P(O or A) = 16/40 + 9/40 - 0 P(O or A) = 25/40 Simplifying, we get: P(O or A) = 5/8 Therefore, the probability of choosing a child with a surname beginning with either O or A is 5/8. Answer: (A) 5/8.