Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Answer:
0.2143 probability that all of them practice satirical.
Step-by-step explanation:
The comedians are chosen without replacement, 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:
8 comedians means that [tex]N = 8[/tex]
6 practice satirical means that [tex]k = 6[/tex]
Sample of 4 means that [tex]n = 4[/tex]
What is the probability that all of them practice satirical?
This is P(X = 4). 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 = 4) = h(4,8,4,6) = \frac{C_{6,4}*C_{2,0}}{C_{8,4}} = 0.2143[/tex]
0.2143 probability that all of them practice satirical.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
