We assume that a dice may only have a Whole Number of sides. (Hypothetical negative-sided or non-integer sided die boggle my mind)
The dice contains all natural numbers up to the number of sides the die has. (So a 6-sided die would have 1,2,3,4,5,6 on its faces)
The coin has a “head” side and “tail” side.
Let X be the number of sides the die has.
Let p be the probability of the coin landing on tails (since the coin was not specified as fair).
There are three hypothetical situations
The Hypothetical Trivial Cases:
X = 0: There is no die, thus you always roll 0 and thus it is dependent solely on the coin flip. Thus the probability is p
X is Even and X > 0
If X is even, the odds of rolling an even number is 1/2, since there is as many even possibilities as odd possibilities
The coin’s odds of landing on tails remains p
Therefore the probability of it being both an even number and landing on tails is: 1/2 * p
X is Odd
If X is odd, there will be 1 more Odd possibility than even possibilities. This can easily be seen with a hypothetical 3-sided die: you can roll a 1 and a 3 for Odd possibilities or you can roll a 2 for Even possibilities. Our odds of getting an even number is number of Even Possibilities divided by Total Possibilities. The number of even possibilities is the same as a die with X-1 sides, while the total number of possibilities is X. We thus have a probability of X being even as ((X-1)/2)/X which simplifies to (X-1)/2X
The coin’s odds of landing on tails still remains p
Therefore the probability of it being both an even number and landing on tails is: p * (X-1)/2X
Answer:
1/2
one half…
Answer:
We Make the Following Assumptions:
We assume that a dice may only have a Whole Number of sides. (Hypothetical negative-sided or non-integer sided die boggle my mind)
The dice contains all natural numbers up to the number of sides the die has. (So a 6-sided die would have 1,2,3,4,5,6 on its faces)
The coin has a “head” side and “tail” side.
Let X be the number of sides the die has.
Let p be the probability of the coin landing on tails (since the coin was not specified as fair).
There are three hypothetical situations
The Hypothetical Trivial Cases:
X = 0: There is no die, thus you always roll 0 and thus it is dependent solely on the coin flip. Thus the probability is p
X is Even and X > 0
If X is even, the odds of rolling an even number is 1/2, since there is as many even possibilities as odd possibilities
The coin’s odds of landing on tails remains p
Therefore the probability of it being both an even number and landing on tails is: 1/2 * p
X is Odd
If X is odd, there will be 1 more Odd possibility than even possibilities. This can easily be seen with a hypothetical 3-sided die: you can roll a 1 and a 3 for Odd possibilities or you can roll a 2 for Even possibilities. Our odds of getting an even number is number of Even Possibilities divided by Total Possibilities. The number of even possibilities is the same as a die with X-1 sides, while the total number of possibilities is X. We thus have a probability of X being even as ((X-1)/2)/X which simplifies to (X-1)/2X
The coin’s odds of landing on tails still remains p
Therefore the probability of it being both an even number and landing on tails is: p * (X-1)/2X
Step-by-step explanation:
Hope you like it!☺️