There are 18 coins total in her bag:
7+3+8=18coins
3 of the 18 coins are dimes, so the odds of first drawing a dime are 3/18
P(dime)=3/18
Since the nickel was taken out and not replaced, there are now 17 coins in her purse.
18-1=17coins
8 of the 17 remaining coins are nickels, so the odds of drawing a nickel are 8/17.
P(nickel)=8/17
Now we multiply the two probabilities by eachother to find out the odds of both occurring...
P(dime)*P(nickel)=
3/18*8/17=24/306=8/103=0.078=8%
The probability of grabbing a dime and then a nickel are 8/103 or 0.078 or an 8% chance, whichever way you'd prefer to write it.
