SOLUTION: a family has 6 children, find the probability that fewer boys and than girls. the probability that any child being a boy is equal to half
Algebra.Com
Question 1102441: a family has 6 children, find the probability that fewer boys and than girls. the probability that any child being a boy is equal to half
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
The probability of having 0 boys is .
The probability of having 1 boy is .
The probability of having 2 boys is .
So the probability of having fewer boys than girls in a family with 6 children is 22/64 = 11/32.
For probability problems like this where there are two outcomes each with probability 1/2 (e.g., gender of children; flipping a fair coin), the easiest and fastest way to get to the answer is using Pascal's Triangle.
The 6th row of Pascal's Triangle is
1 6 15 20 15 6 1
and the sum of the entries is 2^6=64
A quick look at that row tells you the probability is...
1/64 of having 0 boys
6/64 of having 1 boy
15/64 of having 2 boys
20/64 of having 3 boys
15/64 of having 4 boys
6/64 of having 5 boys
1/64 of having 6 boys
RELATED QUESTIONS
Assuming that each child has the probability 0.5 being a boy. Find the probability that a (answered by DrBeeee)
If the probability of any particular child of a family being a boy is 1/2. What is the... (answered by Edwin McCravy)
A family tree has three children. What is the probability that the family has 2 boys and... (answered by ikleyn)
in a family of two children,find the probability that the family has two boys given that... (answered by stanbon)
. If a family has three children, find the probability that it has two girls, given that... (answered by stanbon)
A family has three children , if first child is a boy .What is the probability that... (answered by stanbon)
Assume that the probability is 1/2 that a child born is a boy. What is the probability... (answered by ikleyn)
A family has six children (no twins). What is the probability that this family has three... (answered by Edwin McCravy)
Assume the probability of a boy being born is the same as the probability of a girl being (answered by math_helper)