Final answer:
The probability that Bob will select a quarter from each bag is 5/32.
Step-by-step explanation:
To find the probability that Bob will select a quarter from each bag, we first need to determine the total number of possible outcomes. In the first bag, there are 3 nickels and 5 quarters, so there are a total of 3+5=8 coins. In the second bag, there are 6 nickels and 2 quarters, so there are a total of 6+2=8 coins as well. The total number of possible outcomes is the product of the number of coins in each bag, which is 8*8=64.
Now, let's determine the number of favorable outcomes. Bob needs to select a quarter from the first bag, which is one of the 5 quarters, and a quarter from the second bag, which is one of the 2 quarters. The number of favorable outcomes is the product of the number of quarters in each bag, which is 5*2=10.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: 10/64 = 5/32. Therefore, the probability that Bob will select a quarter from each bag is 5/32.