A box has ten dollars, one is five dollar and four of one dollars. If two bills are chosen at random without replacement, find probability of getting A) amount of valued fifteen dollars B) amount of twelven dollars... is it 4 from 19-15 for A and 7 from 19-12= 7?
I don't understand the question.
In your first sentence, you are saying that there are only 9 dollars in the box.
To solve this problem, we need to understand the concept of probability and how it applies to the given scenario.
Let's break down each part of the question and calculate the probabilities step by step.
A) Probability of getting an amount valued at fifteen dollars:
First, we need to determine the number of favorable outcomes (ways to choose two bills that sum to fifteen dollars) and the total number of possible outcomes (total ways to choose any two bills).
Favorable outcomes:
In this case, we can choose the five-dollar bill and any one-dollar bill to make a total of fifteen dollars. So, there are 4 ways to choose two bills that sum to fifteen dollars.
Total number of possible outcomes:
To calculate the total number of possible outcomes, we consider the number of ways we can choose any two bills from the given options (ten-dollar, five-dollar, and four one-dollar bills). This can be calculated using combinations.
The total number of possible outcomes is calculated as:
C(6, 2) = 6! / (2! * (6 - 2)!)
= 6! / (2! * 4!)
= (6 * 5) / (2 * 1)
= 15
Therefore, the probability of getting an amount valued at fifteen dollars is:
Number of favorable outcomes / Total number of possible outcomes
= 4 / 15
So, your suggestion of 4 from 19-15 is incorrect. The correct probability is 4/15.
B) Probability of getting an amount of twelve dollars:
To find the probability of getting an amount of twelve dollars, we follow a similar approach.
Favorable outcomes:
We can choose the five-dollar bill and any two one-dollar bills to make a total of twelve dollars. So, there are 4 ways to choose two bills that sum to twelve dollars.
Total number of possible outcomes:
Similarly, the total number of possible outcomes can be calculated using combinations.
C(6, 2) = 6! / (2! * (6 - 2)!)
= 6! / (2! * 4!)
= (6 * 5) / (2 * 1)
= 15
Therefore, the probability of getting an amount of twelve dollars is:
Number of favorable outcomes / Total number of possible outcomes
= 4 / 15
So, your suggestion of 7 from 19-12 is incorrect. The correct probability is 4/15 for an amount of twelve dollars.
I hope this explanation helps you understand how to calculate these probabilities using combinations.