Answer:
5/33
Explanation:
From the question, we have the following data:
a. four $5 bills
b. five $10 bills
c. three $20 bills
The total number of dollar ($) bills sponge Bob has is = 4 + 5 + 3 = 12 dollar($) bills in total.
We are asked to find the probability that the first bill he grabs is a $5 bill and , without replacing the $5, the second bill is a $10 bill
Step 1
Find the Probability that Sponge Bob grabs. $5 bill.
Probability = Number of possible outcomes ÷ Number of events.
Number of possible events = four $5 bills
Number of events = 12 dollar bills
P($5 bill) = 4/ 12 = 1/3
Step 2
Find the probability that without replacing the $5, the second bill is a $10 bill
Without replacement of the $5 bill, the total number of dollar bills ( total number of events) reduces and that gives us
Total number of events = 11
Number of possible outcomes = Probability of picking a $10 bill = 5
Therefore, the P($10 bill without replacement ) = 5/11
Step 3
The third and final step is to find the
probability that when he takes his money out of his wallet the first bill he grabs is a $5 bill and , without replacing the $5, the second bill is a $10 bill
This is calculated as:
P($5 bill) × P($10 bill without replacement)
= 1/3 ×5/11
= 5/33
Therefore, the probability that when he takes his money out of his wallet the first bill he grabs is a $5 bill and , without replacing the $5, the second bill is a $10 bill is
5/33