### Answer to pick the higher number

Click here for the question

All the people who answered hit it right.

My only input on this would be to arrive at the same solution in a simpler way with less calculation. As I have said in some of the previous problems, conditional probability could involve some calculations and in some cases this could be avoided. (remember the hidden balls problem).

So the solution:

1. Say Aish picks up a number X.

2. The probability of Abhi picking up the same X is 1/15

3. Apart from the above case, where it could be equal, the chances of Abhi picking a higher number is equal to the chances of Abhi picking a lower number.

4. Hence the probability = (1-1/15)/2 = 7/15

The learning from this is, when there are a set of cases which are mutually exclusive, equally likely and form a comprehensive set, there is a high probability that you have a simpler way of getting the answer than going through conditional probability.

Click here for the question

All the people who answered hit it right.

My only input on this would be to arrive at the same solution in a simpler way with less calculation. As I have said in some of the previous problems, conditional probability could involve some calculations and in some cases this could be avoided. (remember the hidden balls problem).

So the solution:

1. Say Aish picks up a number X.

2. The probability of Abhi picking up the same X is 1/15

3. Apart from the above case, where it could be equal, the chances of Abhi picking a higher number is equal to the chances of Abhi picking a lower number.

4. Hence the probability = (1-1/15)/2 = 7/15

The learning from this is, when there are a set of cases which are mutually exclusive, equally likely and form a comprehensive set, there is a high probability that you have a simpler way of getting the answer than going through conditional probability.

Click here for the question

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