Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Answer:
0.6127 = 61.27% probability of selling no more than 6 properties in one week.
Step-by-step explanation:
For each property, there are only two possible outcomes. Either it is sold, or it is not. The probability of a property being sold is independent of any other property. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
12 properties
This means that [tex]n = 12[/tex]
She feels that there is a 50% chance of selling any one property during a week.
This means that [tex]p = 0.5[/tex]
Compute the probability of selling no more than 6 properties in one week.
This is:
[tex]P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.5)^{0}.(0.5)^{12} = 0.0002[/tex]
[tex]P(X = 1) = C_{12,1}.(0.5)^{1}.(0.5)^{11} = 0.0029[/tex]
[tex]P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161[/tex]
[tex]P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.0537[/tex]
[tex]P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.1208[/tex]
[tex]P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.1934[/tex]
[tex]P(X = 6) = C_{12,6}.(0.5)^{6}.(0.5)^{6} = 0.2256[/tex]
[tex]P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0002 + 0.0029 + 0.0161 + 0.0537 + 0.1208 + 0.1934 + 0.2256 = 0.6127[/tex]
0.6127 = 61.27% probability of selling no more than 6 properties in one week.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
