Get comprehensive answers to your questions with the help of IDNLearn.com's community. Our community provides timely and precise responses to help you understand and solve any issue you face.
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.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.
