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+19 votes

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0

Sir but in this case order will matter.

i.e. If we select 2 and 1 then 2,1 and 1,2 will be treated as different selections.

i.e. If we select 2 and 1 then 2,1 and 1,2 will be treated as different selections.

+5

You don't select both at a time. You select one after the other. So msb1 should be from 7 and then 6 while for msb0 it should be from 6 and then 5. Isn't it so? This way the answer is 0.462.

+4

@kajal sanklecha answer is correct because it is saying independent (not dependent) mean if we choose 1 no. we can choose same no.again and uniform distribution is sufficient to say that probability of sample space is 1 i.e if 1<=n<=13 Probability is 1 otherwise 0.

+12 votes

No of choices with MSB 0 = ( 1, 2, 3, 4, 5, 6, 7}

No of choices with MSB 1 = ( 8, 9, 10, 11, 12, 13}

Since independently assumption is made , Probability = (7*7 + 6*6) / 13*13 = 0.503

The choosing of a number from the set doesn't depend upon the previous selection.

No of choices with MSB 1 = ( 8, 9, 10, 11, 12, 13}

Since independently assumption is made , Probability = (7*7 + 6*6) / 13*13 = 0.503

The choosing of a number from the set doesn't depend upon the previous selection.

+5 votes

Two events are said to be **independent** of each other if the probability of occurrence of the first event does not affect the probability of occurrence of the second event.

So, here it means that whenever we choose one element from the set of 7 elements with MSB 0 for the first time, we can choose one more element from those 7 elements for the second time which gives us 7*7=7^2 favourable outcomes. Similarly, for the case of set of 6 elements with MSB 1, we get 6^6=6^2 more favourable outcomes. So,total favourable outcomes = **7^7 + 6^6** = 85 and the final answer is 85/13^2=**0.502**.

**PS**: I too kept the answer as **(7C2 + 6C2)/(13C2)** = 0.461 in Gate exam but realized the mistake later.

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