it is assumed that when children are born they are equally likely to be boy or girl what is the probability that a family of four children contains three boys and one girl
To calculate the probability of a family of four children containing three boys and one girl, we can use the concept of the binomial distribution.
In this case, we want to find the probability of three successes (boys) in four trials (four children). Assuming each child is equally likely to be a boy or a girl, the probability of having a boy is 0.5 (or 1/2), and the probability of having a girl is also 0.5.
We'll use the formula P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials (4 in this case), k is the number of successes (3 boys), p is the probability of success (0.5), and C(n, k) is the number of combinations of n items taken k at a time (which can be calculated as n! / (k!(n-k)!)).
Plugging in the values, we have:
P(X = 3) = C(4, 3) * 0.5^3 * (1-0.5)^(4-3)
= 4 * 0.5^3 * 0.5^1
= 4 * 0.5^4
= 4 * 0.0625
= 0.25
Therefore, the probability that a family of four children contains three boys and one girl is 0.25 or 25%.
To determine the probability of a family of four children containing three boys and one girl, we can use the concept of probability and the assumption that the probability of a child being a boy or a girl is equal.
Let's consider the possible combinations of children in order to have three boys and one girl:
1) The first child is a boy, the second child is a boy, the third child is a boy, and the fourth child is a girl: BBBG.
2) The first child is a boy, the second child is a boy, the third child is a girl, and the fourth child is a boy: BBGB.
3) The first child is a boy, the second child is a girl, the third child is a boy, and the fourth child is a boy: BGBB.
4) The first child is a girl, the second child is a boy, the third child is a boy, and the fourth child is a boy: GBBB.
The probability of each of these combinations occurring is 1/2 * 1/2 * 1/2 * 1/2 = 1/16.
Since there are four possible combinations that result in three boys and one girl, we can add up their probabilities:
1/16 + 1/16 + 1/16 + 1/16 = 4/16 = 1/4
Therefore, the probability that a family of four children contains three boys and one girl is 1/4 or 25%.
To determine the probability that a family of four children contains three boys and one girl, we can use the concept of the binomial distribution. In this case, each child has two possible outcomes: boy or girl.
The formula for the binomial distribution is:
P(X=k) = C(n, k) * p^k * q^(n-k)
Where:
P(X=k) is the probability of getting exactly k successes (boys in this case),
n is the total number of trials (number of children),
k is the number of successes (number of boys),
p is the probability of success (probability of having a boy), and
q is the probability of failure (probability of having a girl).
In this case, n = 4 (total number of children), k = 3 (number of boys), p = 1/2 (probability of having a boy), and q = 1/2 (probability of having a girl).
Substituting these values into the formula, we get:
P(X=3) = C(4, 3) * (1/2)^3 * (1/2)^(4-3)
The expression C(4, 3) represents the number of ways to choose 3 boys out of 4 children and can be calculated as:
C(4, 3) = 4! / (3!(4-3)!) = 4
Evaluating the expression, we have:
P(X=3) = 4 * (1/8) * (1/2) = 4/16 = 1/4
Therefore, the probability that a family of four children contains three boys and one girl is 1/4 or 25%.