Question

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 HELP PLEASE THIS IS FOR PLATO.

Answer 1

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

2/3

Explanation:

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