A Box containing coins question

If a box contains 4 pennies, 4 nickels, 4 dimes and 2 coins are selected at random WITH replacement and D (>=0) is the numerical difference between their values (meaning if a nickel is chosen then only a nickel or dime can be chosen not a penny) what is the probability function of D, f(x)=P(D=x).

Thanks in advance


TS Contributor
Again no TSer understand the definition of \( D \) yet. Please provide a precise mathematical definition for it.

Or at least you list the outcomes with different scenarios.

e.g. What will \( D \) equals to when you have

- penny + nickel
- dime + nickel
- penny + dime
- 2 pennies
- 2 nickels
- 2 dimes

Answering all these will be a definition too.
- penny + nickel=11
- dime + nickel=15
- penny + dime=11
- 2 pennies=2
- 2 nickels=10
- 2 dimes=20

But the question is saying 2 coins are chosen, what is the probability that the numerical difference between them is greater than or equal to 0 which means that when the first coin is chosen that the second coin thats chosen MUST be either the same as the first or LARGER than it.


Ambassador to the humans
Is the wording in the original post the exact wording of the problem you were giving or did you add some stuff?

Specifically I'm wonder if "meaning if a nickel is chosen then only a nickel or dime can be chosen not a penny" was something you added or if it was in the problem statement.
I've never seen notation like D(>=) and am not sure if I understand the question, but if you are asking: "Drawing two coins with replacement, what is the probability the second coin is greater than or equal to the first coin"

There are 9 equally likely outcomes

(1,1) (1,5) (1,10) (5,1) (5,5) (5,10) (10,1) (10,5) (10,10)

Six of the outcomes the the first coin is greater than or equal to the second

(1,1) (5,1) (5,5) (10,1) (10,5) (10,10)


Just my two cents


Ambassador to the humans
Note however that your question is asking for the pdf of D. So that really doesn't give you a complete answer. Honestly I'm not sure it's being interpreted correctly but you'd have to ask your instructor what it really should mean. I highly doubt your instructor's intent is to confuse you on what the random variable actually is.