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 then 30 cents in it?
To have more than 30 cents, the right pocket must have the quarter and the dime.
possible cases, order does not matter:
L --- left pocket, R -- right pocket
L -- R
QP ND
QN PD
QD PN
PN QD
PD QN
ND QP -----> so we have 6 cases
prob = 1/6
To find the probability that the front right pocket has more than 30 cents in it, we need to determine the different combinations of coins that can result in more than 30 cents in the front right pocket.
Let's first list all the possible combinations of coins we can have in the front right pocket:
1. Penny and nickel
2. Penny and dime
3. Penny and quarter
4. Nickel and dime
5. Nickel and quarter
6. Dime and quarter
Out of these six combinations, only three combinations result in more than 30 cents in the front right pocket:
1. Penny and dime
2. Penny and quarter
3. Nickel and quarter
Now, let's calculate the probability.
The student has a total of 4 coins to distribute between the two pockets. In the front right pocket, there are two possible coin combinations that give more than 30 cents. Therefore, the probability can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 3 / 6
Probability = 1/2
So, the probability that the front right pocket has more than 30 cents in it is 1/2.