SOLUTION: If a family is planning to have 6 Children, what is the probability of having:
1) 5 boys, 1 girl
2) 3 girls, 3 boys
Algebra.Com
Question 1026994: If a family is planning to have 6 Children, what is the probability of having:
1) 5 boys, 1 girl
2) 3 girls, 3 boys
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
If a family is planning to have 6 Children, what is the probability of having:
1) 5 boys, 1 girl
2) 3 girls, 3 boys
Solution:
Assume equal probabilities of having girls and boys.
This problem can be solved by drawing a binary probability tree with 64 ultimate branches, and the required answer by counting.
Alternative to the tree, it could be a table 6 rows (usually columns, but here I put them in rows to make typing easier).
BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBG
BBGGBBGGBBGGBBGGBBGGBBGGBBGGBBGGBBGGBBGGBBGGBBGGBBGGBBGGBBGGBBGG
BBBBGGGGBBBBGGGGBBBBGGGGBBBBGGGGBBBBGGGGBBBBGGGGBBBBGGGGBBBBGGGG
BBBBBBBBGGGGGGGGBBBBBBBBGGGGGGGGBBBBBBBBGGGGGGGGBBBBBBBBGGGGGGGG
BBBBBBBBBBBBBBBBGGGGGGGGGGGGGGGGBBBBBBBBBBBBBBBBGGGGGGGGGGGGGGGG
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
From the above table, seek out the cases where there are 5 boys and 1 girl, or 3 girls and 3 boys. (Each column represents one case, 64 columns in all).
If you find this method to straining to your eyes, you can always try the binomial probability distribution, which says that
P(x,n,p)=
where
x is the number of boys
n is the total number of children (6)
p is the probability of having a boy (0.5)
and
C(n,x) is the binomial coefficient of taking x objects out of n, and equals
n!/(x!(n-x)!)
Hence
(1) P(5 boys, 6,0.5) =
(2) P(3 boys, 6,0.5) =
RELATED QUESTIONS
a family has 5 children. the probabilty of having a girl is 1/2. what is the probabilty... (answered by stanbon)
Suppose that a family has 5 children. Also, suppose that the probability of having a girl (answered by stanbon)
A family has five children. The probability of having a girl is 1/2.what is the... (answered by fractalier)
A family has five children. The probablilty of having a girl is 1/2. What is the... (answered by stanbon)
In a family of three children there are 8 possibilities for the boy-girl combinations,... (answered by stanbon)
If a single family having one girl is 1/2, then what is probability of a family with 3... (answered by Boreal)
Assume that each child that is born is equally likely to be a boy or girl . If a family... (answered by ikleyn)
if the probability of a child being a girl is 1/2, and a family plans to have 4 children, (answered by htmentor)
n a family with 5 children what is the probability of having 3 boys and then 2 girls, in... (answered by Edwin McCravy,greenestamps)