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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

### 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

[i]
[i]