A probability problem by atishay jain
A chooses a two digit number with non-zero digits. B has 9 chances to guess what two digit number it is. Each time B makes a guess and the answer is wrong, A will tell him how many digits are correct.
To 2 decimal places, what is the probability that B would be able to guess the correct number?
The answer is 1.00.
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1 solution
The answer is 1 i.e. (B) will surely be able to guess (A)'s no.
(B) can guess the no. in the sequence shown: 12 13 14 15 16 17 18 now, (B) has tried 7 no. which have a possibility to be correct but we have to find in the worst case. (A) will tell the no. of correct digits in (B)'s guess. So from these no.s (B) will be sure about the digits used in the no., (A) chooses. Now (B) will try those digits but the digits could have been in reverse order so in the next turn (B) will be able to tell the correct no.
for example, let say (A) chooses the no. 94 Now, (B) will guess in the sequence
similarly, (B) will try rest numbers of the sequence and will get know that only 9 is the other possible digit So (B) can firstly try 49 i.e not correct. While the next try (B) will be able to guess correct no. i.e.94 in 9 chances.