Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Answer:
31.82% probability that you will receive 2 apples.
Step-by-step explanation:
The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
5 + 7 = 12 total fruits, which means that [tex]N = 12[/tex]
7 apples, which means that [tex]k = 7[/tex]
You receive 2 fruits, which means that [tex]n = 2[/tex]
What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?
This is, as a proportion, P(X = 2). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,12,2,7) = \frac{C_{7,2}*C_{5,0}}{C_{12,2}} = 0.3182[/tex]
0.3182*100% = 31.82%
31.82% probability that you will receive 2 apples.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.