Read slowly.

Probability Level 4

A letter is known to have come from CHENNAI, JAIPUR, NAINITAL, MUMBAI. Your mother receives the letter and she randomly tells you two consecutive alphabets. If she tells you AI, then find the probability that it came from MUMBAI (rounded off up to 3 decimal places).

The answer is 0.282.

1 solution

Cody Martin
Feb 20, 2015

probability that letter is from chennai=0.25, probability that letter is from mumbai=0.25, probability that letter is from jaipur=0.25, probability that letter is from nainital=0.25,

probability of having AI consecutive in chennai=0.166, probability of having AI consecutive in jaipur=0.2, probability of having AI consecutive in nainital=0.142, probability of having AI consecutive in mumbai=0.2,

now by using bayes theorem we can find out the probability of letter belonging to mumbai and having ai letters consecutive

$\frac{ \frac{ 1 }{ 4 }*\frac{ 1 }{ 5 } }{ \frac{ 1 }{ 4 }*\frac{ 1 }{ 6 }+\frac{ 1 }{ 4 }*\frac{ 1 }{ 5 }+\frac{ 1 }{ 4 }*\frac{ 1 }{ 7 }+\frac{ 1 }{ 4 }*\frac{ 1 }{ 5 } }$ =0.282

It is not mentioned that two consecutive letters are randomly visible! The answer should be $0.25$ . If it's said that in the given word, two consecutive letters are randomly visible, AND they turn out to be $AI$ , then the answer is as given.

Consider the following:

Q1. A letter is known to have come from CHENNAI, JAIPUR, NAINITAL or MUMBAI. But when the letter arrives, it is received by your friend. When you ask your friend where the letter came from, she randomly selects two consecutive letters from the name and tells you. If the letters she tells you are $AI$ , find the probability that it came from MUMBAI. Ans.=0.282

Q2. A letter is known to have come from CHENNAI, JAIPUR, NAINITAL or MUMBAI. But when the letter arrives, it is received by your friend. She blacks out everything other than $AI$ , regardless of the name. Then she gives the letter to you. Find the probability that it came from MUMBAI. Ans.=0.25

EDIT: the question was rephrased after this comment. it is now perfectly right. and is same as Q1.

Raghav Vaidyanathan - 6 years, 3 months ago

i support your argument but lets see what would happen if we consider your second case: 1)the given question would have become an overrated question as there would be no use of bayes theorem 2) the solution given to a similar problem in many class XII reference books would be wrong

Cody Martin - 6 years, 3 months ago

I answered when the question was unrated. It became level 5 as soon as i got it wrong. And the questions given in NCERT are all well worded and correct.

Raghav Vaidyanathan - 6 years, 3 months ago

YOU'RE RIGHT....TOTALLY....It should be 0.25

Saaket Sharma - 6 years, 3 months ago

no, refer to my comment again. and disputes.

Raghav Vaidyanathan - 6 years, 3 months ago

This was such a beautiful problem, I failed in the first try because of idiotically considering the number of ways of selection A and I together out of total pairs, then i realised that i must only consider consecutive pairs and got the right answer

Mvs Saketh - 6 years, 3 months ago

Read slowly.

The answer is 0.282.

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