Problem: You are in a dicey situation. You friend gave you a dice and asked you to keep rolling till you get a sum of 100 or more. Now,you have to tell the most probable number at which you are going to stop.
Solution: You will stop at or before 105. Now, trick is to think backwards. You can get 105, only if you ever reach 99. Similarly, you can get 104, only from 99 or 98. You can get to 100, from maximum previous sums i.e. 94, 95, 96, 97, 98 and 99. Therefore, 100 is the most probable stopping point. P(105) = P(105|99).P(99) = P(99)/6 . Similiarly, P(104) = (P(99)+P(98))/6, ...P(100) = (P(94)+...+P(99))/6
Source: Rishab
Solution: You will stop at or before 105. Now, trick is to think backwards. You can get 105, only if you ever reach 99. Similarly, you can get 104, only from 99 or 98. You can get to 100, from maximum previous sums i.e. 94, 95, 96, 97, 98 and 99. Therefore, 100 is the most probable stopping point. P(105) = P(105|99).P(99) = P(99)/6 . Similiarly, P(104) = (P(99)+P(98))/6, ...P(100) = (P(94)+...+P(99))/6
Source: Rishab
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