Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Answer:
0.3125 = 31.25% probability that it is not ideal.
Step-by-step explanation:
For each children, there are only two possible outcomes. Either it is a girl, or they are not. The probability of a child being a girl is independent of any other child. 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.
0.5 probability of a children being a girl:
This means that [tex]p = 0.5[/tex]
If you randomly select a Happyville family that has four children, what is the probability that it is not ideal?
Not ideal is less than two girls, so this is P(X < 2).
Four children means that [tex]n = 4[/tex]. So
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.5)^{0}.(0.5)^{4} = 0.0625[/tex]
[tex]P(X = 1) = C_{4,1}.(0.5)^{1}.(0.5)^{3} = 0.25[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0625 + 0.25 = 0.3125[/tex]
0.3125 = 31.25% probability that it is not ideal.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
