All students in Peter's class have $1.05, consisting of nickels and/or dimes and/or quarters. Each student has a different combination of coins, and all possible combinations of coins are included. What is the probability that Peter is unable to give his friend Jenny change for $1.00?
To find the probability that Peter is unable to give his friend Jenny change for $1.00, we need to consider two things: the possible combinations of coins that Peter could have and the possible combinations of coins that would add up to exactly $1.00.
Let's start by listing all the possible combinations of coins that Peter could have. Since each student has a different combination and all possible combinations are included, we can assume that Peter could have any combination of coins except for one combination which adds up to $1.00.
Since we know that Peter has $1.05, let's consider the different options he could have:
Option 1: Peter has 5 nickels (5 cents each). In this case, Peter cannot give Jenny $1.00 since nickels cannot be combined to make a whole dollar.
Option 2: Peter has 10 dimes (10 cents each). In this case, Peter can give Jenny $1.00 since 10 dimes make a dollar.
Option 3: Peter has 4 quarters (25 cents each) and 1 nickel (5 cents). In this case, Peter cannot give Jenny $1.00 since 4 quarters and 1 nickel only add up to $1.05.
So there are 3 possible combinations of coins that Peter could have.
Now let's consider the possible combinations of coins that would add up to exactly $1.00:
Option 1: 100 pennies (1 cent each).
Option 2: 4 quarters (25 cents each).
Option 3: 10 dimes (10 cents each).
So there are 3 possible combinations of coins that would add up to exactly $1.00.
Since there are 3 possible combinations of coins that Peter could have and 3 possible combinations of coins that would add up to exactly $1.00, the probability that Peter is unable to give his friend Jenny change for $1.00 is 1 out of 3, or 1/3.