it is assumed that when children are born they are equally likely to be boys or girls what is probability that a family of four children contain two boys two girls
To find the probability of a family of four children containing two boys and two girls, we can use the concept of binomial probability.
The probability of a single birth event resulting in a boy is 0.5 (equally likely to be a boy or girl). Therefore, the probability of having two boys and two girls in a four-child family can be calculated using the binomial coefficient formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
n = number of trials (total number of children)
k = number of successes (desired outcome)
p = probability of success (probability of having a boy)
In this case, n = 4 (total number of children), k = 2 (number of boys), and p = 0.5.
P(X=2) = (4 choose 2) * 0.5^2 * (1-0.5)^(4-2)
= (6) * 0.25 * 0.25
= 0.09375
Therefore, the probability that a family of four children contains two boys and two girls is 0.09375 or 9.375%.
To find the probability that a family of four children contains two boys and two girls, we can use the binomial probability formula.
The formula for the binomial probability is:
P(x) = C(n, x) * p^x * (1-p)^(n-x)
Where:
P(x) is the probability of getting x successes in n trials
C(n, x) is the number of combinations of n items taken x at a time
p is the probability of success on a given trial
n is the number of trials
In this case, the probability of having a boy or a girl is the same (0.5 for each) since they are equally likely. So, p = 0.5.
We want to find the probability of having 2 boys and 2 girls, which means we want to find P(2).
Substituting the values into the formula:
P(2) = C(4, 2) * 0.5^2 * (1-0.5)^(4-2)
Calculating each part:
C(4, 2) = 4! / (2! * (4-2)!) = 6
0.5^2 = 0.25
(1-0.5)^(4-2) = 0.25
So, the probability P(2) = 6 * 0.25 * 0.25 = 0.375.
Therefore, the probability that a family of four children contains two boys and two girls is 0.375 or 37.5%.
To find the probability that a family of four children contains two boys and two girls, we can use the concept of combinations and the assumption that each child has an equal chance of being a boy or a girl.
First, let's calculate the total number of possible outcomes for the family of four children. Since each child can either be a boy or a girl, there are two possible outcomes (boy or girl) for each child. Therefore, the total number of possible outcomes is 2 multiplied by itself four times (2^4), which equals 16.
Now, let's determine the number of favorable outcomes, which in this case is the number of ways we can have two boys and two girls in a family of four children.
To calculate this, we can use the combination formula. The number of ways to choose "k" objects from "n" objects without regard to the order is given by the formula:
C(n, k) = n! / (k!(n-k)!)
In this case, we need to calculate C(4,2), which represents the number of ways to choose 2 boys out of 4 children:
C(4,2) = 4! / (2!(4-2)!) = (4 * 3) / (2 * 1) = 6
Since we also want to count the number of ways to choose 2 girls out of the remaining 2 children:
C(2,2) = 2! / (2!(2-2)!) = 1
Now, we can multiply the two combinations together to get the total number of favorable outcomes:
6 * 1 = 6
Finally, we divide the number of favorable outcomes (6) by the total number of possible outcomes (16) to find the probability:
Probability = Favorable outcomes / Total outcomes = 6 / 16 = 3 / 8
So, the probability that a family of four children contains two boys and two girls is 3/8.