Cathy has a nickel, a dime, and a quarter in her purse. she randomly picks a coin, replaces it, and then picks another coin. the probability that the two coins are of different denominations is .
someone this is for plato.

Hence, the probability that the two coins are of different denomination is:

                            2/3

Let N denote nickel, D denotes dime and Q denotes Quarter.

Now when two coins are drawn one after the other with replacement then the outcomes is given by:

         (N,N)     (N,D)      (N,Q)

         (D,N)     (D,D)      (D,Q)

         (Q,N)     (Q,D)      (Q,Q)  

This means that there are a total of  9 outcomes.

The outcomes such that both the denominations are different i.e. the number of favorable outcomes are:  6

{ (N,D) (N,Q) (D,N) (D,Q) (Q,N) (Q,D) }

The probability that the two coins are of different denomination is:

                             6/9=2/3

step-by-step explanation:

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step-by-step explanation: