Riddles Options

[shivani]

1. Guess the next number

77 58 49 45 29 27 23

[vivekpm]

There are three scenarios to consider here:

1. Person 1 takes his seat(probability=1/50): In this case, last person will definately get his seat (probability=1)
2. Person 1 takes 50th person's seat(probability=1/50): In this case,last person will definately not get his seat (probability=0)
3. Person 1 takes any other seat apart from 1st and 50th(probability=48/50), in this case probability of last person getting his seat is 0.5 because:
   • Person whose seat is taken may take 50th seat or 1st seat or any other seat. And this will continue until someone either selects 50th seat or 1st seat in which case problem is solved. Probability of selecting one out of 1st and 50th seat is 0.5.

So now, from 1,2 and 3:

1/50*1+1/50*0+48/50*0.5=0.2+0.48=0.5

So the answer is 0.5.

Cheers,