Charlie's wallet contains 3 ones, 2 fives, 2 tens, and 4 twenty dollar bills. ?Charlie randomly grabs a bill from his wallet, replaces it, and grabs another bill. What is the probability that the sum of the two bills is $25? Maybe 6/25 or 6/110. I am confusing myself now and I really need help. The first time I came up with 8/121. I don't know anymore. Please help me
To solve this problem, we need to find the probability of two bills being chosen from Charlie's wallet that sum up to $25. Charlie's wallet contains several bills of different denominations: 1 dollar bills, 5 dollar bills, 10 dollar bills, and 20 dollar bills.
Let's break down the problem into steps:
Step 1: Find the total number of possible combinations
In this case, Charlie randomly selects two bills from his wallet. To calculate the total number of possible combinations, we need to multiply the number of choices for the first bill by the number of choices for the second bill.
There are a total of 11 bills in Charlie's wallet:
3 ones, 2 fives, 2 tens, and 4 twenties.
So the total number of possible combinations is: 11 * 11 = 121
Step 2: Find the favorable combinations
Now, let's determine the total number of combinations that result in a sum of $25. We'll go through each possible combination and calculate their sums.
Combination 1: Two twenties (20 + 20 = 40) - Not a favorable combination.
Combination 2: One twenty + One five (20 + 5 = 25) - This is a favorable combination.
Combination 3: One twenty + One ten (20 + 10 = 30) - Not a favorable combination.
Combination 4: One twenty + One one (20 + 1 = 21) - Not a favorable combination.
Combination 5: Two tens (10 + 10 = 20) - Not a favorable combination.
Combination 6: One ten + One five (10 + 5 = 15) - Not a favorable combination.
Combination 7: One ten + One one (10 + 1 = 11) - Not a favorable combination.
Combination 8: Two fives (5 + 5 = 10) - Not a favorable combination.
Combination 9: One five + One one (5 + 1 = 6) - Not a favorable combination.
Combination 10: Two ones (1 + 1 = 2) - Not a favorable combination.
So, there is only 1 favorable combination that results in a sum of $25.
Step 3: Calculate the probability
The probability of an event occurring is given by the number of favorable outcomes divided by the total number of possible outcomes.
In our case, there is 1 favorable combination and 121 total possible combinations.
Therefore, the probability is: 1/121.
So, the correct answer is 1/121, not 6/25 or 6/110 as you mentioned earlier.
11 bills in all
The two bills must be 5,20 or 20,5
p = (2/11 * 4/10) + (4/11 * 2/10) = 8/55