3 ms·
>> From a fundamentals perspective, the expected number of meals is a function of the probability of finding the fourth toy in any specific meal. > I can barel
by kgwgk 4y ago
>> From a fundamentals perspective, the expected number of meals is a function of the probability of finding the fourth toy in any specific meal.
> I can barely parse it. The probability of finding the nth toy before the nth meal is 0, so is the answer a function of 0?
The probability of finding the fourth toy in the first meal is 0%.
The probability of finding the fourth toy in the second meal is 0%.
The probability of finding the fourth toy in the third meal is 0%.
The probability of finding the fourth toy in the fourth meal is 9.4% or whatever.
The probability of finding the fourth toy in the fifth meal is 37.5% or whatever.
Etc.
The expected number of meals is 1 x 0% + 2 x 0% + 3 x 0% + 4 x 9.4% + 5 x 37.5% + 6 x ... + ...
- deleted 4y ago[deleted]
- kgwgk 4y agoMore precisely: The probability of finding the fourth toy in the first meal is 0%. The probability of finding the fourth toy in the second meal is 0%. The probability of finding the fourth toy in the third meal is 0%. The probability of finding the fourth toy in the fourth meal is 3/32 = 9.4%. The probability of finding the fourth toy in the fifth meal is 9/64 = 14.1%. The probability of finding the fourth toy in the sixth meal is 123/512 = 24.0%. The probability of finding the fourth toy in the seventh meal is 135/1024 = 12.0%. The probability of finding the fourth toy in the eighth meal is 903/8192 = 11.0%. The probability of finding the fourth toy in the ninth meal is 1449/16384 = 8.8%. Etc. The expected number of meals is 1 x 0% + 2 x 0% + 3 x 0% + 4 x 9.4% + 5 x 14.1% + 6 x 24.0% + 7 x 12.0% + 8 x 11.0% + 9 x 8.8% + ...