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Oliveboard Question of the day
Ishan being dyslexic, gets confused between the following pairs/sets of letters and writes them interchangeably: (B & D); (U, V & W); (E & F). He gets punished by his teacher whenever he makes three or more mistakes in a single word. Find the probability that he’ll get punished if he’s asked to write the word ‘OLIVEBOARD’. (Assume he makes no other mistake)
Options:
(a) 3/8
(b) 5/24
(c) 1/12
(d) None of these
Solution posted below. Click on the plus sign to view the solution.
Answer and Explanation
Answer key: a
As per the given conditions, he can possibly make mistake at four places
A – Letter V
B – Letter E
C – Letter B
D – Letter D
Let P(A), P(B), P(C) and P(D) denote the probabilities that he makes the above mistakes respectively.
P(A) = 2/3, P(B) = 1/2, P(C) = 1/2 and P(D) = 1/2.
Probability that he gets punished = P(A B C D) + P(A B C D) + P(A B C D) + P(A B C D) + P(A B C D)
= (2/3*1/2*1/2*1/2) + (2/3*1/2*1/2*1/2) + (2/3*1/2*1/2*1/2) + (1/3*1/2*1/2*1/2) + (2/3*1/2*1/2*1/2)
= 3/8
It should be d.
d.none 9/24
c
1/12
5/24