What the fox say?
Number Theory
Level
3
A man is trying to predict what a fox will say given a specific integer from 1 to 100. He is given the following criteria:
- For any number divisible by 11, the fox will say Ringalingding.
- For any number not divisible by 11, the fox will flip a weighted coin times where the number given as an input and , the probability of getting heads, is determined by the number of coins left to roll/100. If the number of heads is 5 times the number of tails, the fox will say nothing. Otherwise, it will say Ringalingding.
What is the probability that the fox says Ringalingding?
More than 80%
Between 50 and 75%
Less than 50%
Less than 9%
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1 solution
The probability of getting heads is immaterial in this case. The only way the fox says nothing is if the number of heads he flips is 5 times the number of tails; but this can only happen if the number of flips is a multiple of 6. There are only 16 multiples of 6 among the integers from 1 to 100, and one of them, 66, is a multiple of 11. Thus there is only a 15% chance there will even be the possibility the fox says nothing; so even if the number of heads is indeed 5 times the number of tails every time this can happen, the fox will still say Ringalingading 85% of the time.