A student has a penny, nickel, dime, and quarter distributed

two coins apiece to his front two pants pockets.
What is the probability that the front right pocket has more than 30¢ in it?

Can you show all work, I am acting as a school teacher who is teaching this problem to elementary students, thanks.

"the front right pocket has more than 30¢ in it"

More than 30¢ implies you can only have a dime and a quarter.

The first coin has to be a dime or a quarter out of 4 coins, so the probability is 2/4. The second coin has to be one choice out of three, so it is 1/3.

We want the both events to occur, so the probability is the product of the probabilities of the individual events, namely:
(2/4)*(1/3)
=1/6

Sure, I'd be happy to show you the step-by-step process of solving this problem.

To find the probability that the front right pocket has more than 30¢ in it, we first need to identify all the possible combinations of coins that can go into each pocket.

Since there are two coins in each pocket, we can distribute them in the following ways:

1. Penny and Nickel in Front Right, Dime and Quarter in Front Left
2. Penny and Dime in Front Right, Nickel and Quarter in Front Left
3. Penny and Quarter in Front Right, Nickel and Dime in Front Left
4. Nickel and Dime in Front Right, Penny and Quarter in Front Left
5. Nickel and Quarter in Front Right, Penny and Dime in Front Left
6. Dime and Quarter in Front Right, Penny and Nickel in Front Left

Now, let's determine the value of each combination:

1. Penny (1¢) + Nickel (5¢) = 6¢
2. Penny (1¢) + Dime (10¢) = 11¢
3. Penny (1¢) + Quarter (25¢) = 26¢
4. Nickel (5¢) + Dime (10¢) = 15¢
5. Nickel (5¢) + Quarter (25¢) = 30¢
6. Dime (10¢) + Quarter (25¢) = 35¢

Out of these six combinations, we can see that only one combination (Dime and Quarter in Front Right) has more than 30¢.

Therefore, the probability that the front right pocket has more than 30¢ is 1 out of 6, which can be simplified to 1/6 or approximately 0.1667.

I hope this explanation helps, and please let me know if you have any further questions!