The Wilson family had 9 children. Assuming that the probability of a child being a girl...

The Wilson family had 9 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had: at least 2 girls? at most 3 girls? Round your answers to 4 decimal places.

Solutions

Expert Solution

X : Number of girl children that Wilson Family had

Number of children Wilson family had : n = 9

Probability of a child being a girl :p = 0.5

X follows a Binomial distribution with n=9 and p=0.5 (q=1-p=1-0.5=0.5)

Probability that Wilson Family had 'r' girl children = P(X=r)

Probability that the Wilson family had at least 2 girls = P(X2)

P(X2) = 1 - P(X<2) = 1-P(X1)

P(X1) = P(X=0)+P(X=1)

P(X1) = P(X=0)+P(X=1) = 0.001953125+0.017578125 = 0.01953125

P(X2) = 1 - P(X<2) = 1-P(X1) = 1-0.01953125 =0.98046875

Probability that the Wilson family had at least 2 girls = P(X2) = 0.98046875

Probability that the Wilson family had at least 2 girls = 0.9805

Probability that the Wilson family had at most 3 girls = P(X 3)

P(X 3) = P(X=0)+P(X=1)+P(X=2)+P(X=3)

P(X 3) = P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.001953125+0.017578125+0.0703125+0.1640625=0.25390625

Probability that the Wilson family had at most 3 girls = P(X 3) = 0.25390625

Probability that the Wilson family had at most 3 girls = 0.2539

milcah answered 7 months ago

Next > < Previous

Related Solutions

The Wilson family had 7 children. Assuming that the probability of a child being a girl...

The Wilson family had 7 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had at least 6 girls? at most 6 girls? Round your answers to 3 decimal places.

Helen has two children. Assume that the probability of each child being a girl is 50%,...

Helen has two children. Assume that the probability of each child being a girl is 50%, and is independent with the gender of the other child. Given that at least one of Helen’s children is a girl, what is the probability that the other child is a boy? (A) 1/3 (B) 1/2 (C) 2/3 (D) 3/4 (SHOW WORK)

A family has 4 children. Assume that each child is as likely to be a boy as it is to be a girl.

A family has 4 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 4 girls if it is known the family has at least one girl.

1. Assumptions: Two child family, the probability of a boy or girl is .5, sex of...

1. Assumptions: Two child family, the probability of a boy or girl is .5, sex of one child in the family is independent of the sex of the other child. Case A: With no other information given, what is the probability that a family has 2 girls? Case B: A family has at least 1 girl, what is the probability that a family has 2 girls? Case C: A family has at least 1 girl who is its first born...

Estimate, by simulation, the average number of children there would be in a family if all people had children until they had a girl.

in R. Estimate, by simulation, the average number of children there would be in a family if all people had children until they had a girl. Do the same if all people had children until they had at least one boy and at least one girl. How many more children would you expect to find under the second scheme than under the first in 100,000 families? (Assume that girls and boys are equally likely.)

Consider a family with 4 children. Assume the probability that one child is a boy is...

Consider a family with 4 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events "boy" and "girl" are independent. (a) List the equally likely events for the gender of the 4 children, from oldest to youngest. (Let M represent a boy (male) and F represent a girl (female). Select all that apply.) FMMFone M, three F'sFFFFMMMMFMFMFMFFtwo M's, two F'sthree M's, one...

In a family of 4 children, what is the probability that two of the children are...

In a family of 4 children, what is the probability that two of the children are boys and two of the children are girls? answer correct to 4 decimal places

A family decides to have children until it has three male children. Assuming ?(????) = ?(??????)...

A family decides to have children until it has three male children. Assuming ?(????) = ?(??????) = 0.5, a. what is the probability that the family has ? female children? b. Calculate ?(?) and ?(?).

Assuming that in some part of Quebec the probability is 0.00007 that a child will develop...

Assuming that in some part of Quebec the probability is 0.00007 that a child will develop cancer. Therefore, the number Z among 28, 572 children that will develop cancer follows a Binomial distribution with parameters p = 0.00007 and n = 28, 572. We would like to use the Poisson distribution to approximate these binomial probabilities. (a) What is the adequate value of the variance of the Poisson distribution to use in order to approximate the precedent binomial distribution? (b)...

in a certain country, the true probability of a baby being a girl is 0.464. Among...

in a certain country, the true probability of a baby being a girl is 0.464. Among the next nine randomly selected births in the country, what is the probability that at least one of them is a boy?

Subjects