A money envelope contains five $10

Question

bills, ten $20
bills, and fifteen $50
bills. Sandra randomly selects two bills without returning the first bill. What is the probability of getting a $10
bill then a $50
bill? Write your answer in the simplest form of fraction.(1 point)

Answer 1

To find the probability of selecting a $10 bill followed by a $50 bill without replacement, we can follow these steps:

1. Count the Total Number of Bills:

   • Number of $10 bills = 5
   • Number of $20 bills = 10
   • Number of $50 bills = 15
   • Total number of bills = 5 + 10 + 15 = 30

2. Calculate the Probability of Selecting a $10 Bill First:

   • Probability of selecting a $10 bill = Number of $10 bills / Total number of bills \[ P(10) = \frac{5}{30} = \frac{1}{6} \]

3. Update the Total Number of Bills After Selecting a $10 Bill:

   • After selecting one $10 bill, the remaining number of bills = 30 - 1 = 29

4. Calculate the Probability of Selecting a $50 Bill Second:

   • Number of $50 bills remains 15 (since we selected a $10 bill).
   • Probability of selecting a $50 bill now = Number of $50 bills / Remaining total number of bills \[ P(50 | 10) = \frac{15}{29} \]

5. Compute the Joint Probability of Both Events:

   • The total probability of selecting a $10 bill followed by a $50 bill is the product of the two probabilities: \[ P(10 \text{ and then } 50) = P(10) \cdot P(50 | 10) = \frac{1}{6} \cdot \frac{15}{29} \]

   Multiplying the fractions: \[ P(10 \text{ and then } 50) = \frac{1 \cdot 15}{6 \cdot 29} = \frac{15}{174} \]

6. Simplify the Fraction:

   • Now we simplify \(\frac{15}{174}\). The greatest common divisor (GCD) of 15 and 174 is 3. \[ \frac{15 \div 3}{174 \div 3} = \frac{5}{58} \]

Thus, the probability of getting a $10 bill followed by a $50 bill is \(\boxed{\frac{5}{58}}\).