Let's solve the word problem step by step to find the probability of randomly choosing a one-dollar bill from your pocket.
1. Identify the total number of bills in your pocket:
You have:
- 2 one-dollar bills
- 1 five-dollar bill
So, the total number of bills is:
[tex]\[
\text{Total bills} = 2 + 1 = 3
\][/tex]
2. Determine the number of favorable outcomes:
The favorable outcome here is choosing a one-dollar bill. You have 2 one-dollar bills.
So, the number of favorable outcomes is:
[tex]\[
\text{One-dollar bills} = 2
\][/tex]
3. Calculate the probability:
The probability [tex]\( P \)[/tex] of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
Hence, the probability of randomly choosing a one-dollar bill is:
[tex]\[
P(\$1) = \frac{\text{Number of one-dollar bills}}{\text{Total number of bills}} = \frac{2}{3}
\][/tex]
Therefore, the probability that you randomly choose a one-dollar bill from your pocket is [tex]\( \frac{2}{3} \)[/tex].
