Question

Three numbers are chosen from 1 to 30 randomly. The probability that they are not consecutive is: option 1 : 1/145 option 2 : 144/145 option 3 : 139/140 option 4 : 1/140

Answer 1

If the three numbers have to be consecutive:

Then the favorable outcomes would be

(1,2,3),(2,3,4).....(27,28,29),(28,29,30) i.e. 28 outcomes.

Now the total no. of outcomes would be:

We have to select 3 nos. out of 30 nos. irrespective of the order of the numbers.

Therefore, the total number of outcomes would be 30C3.

The probability would be 28/30C3 which will give us 1/145.

The answer will be 1/145.