It is assume that when they children are born they are equally likely to be boys or girl what is the probability that a family of four children contain three boys and one girl
To find the probability that a family of four children contains three boys and one girl, we can use the binomial probability formula.
The formula for calculating the probability of exactly k successes in n independent Bernoulli trials, where each trial has a probability p of success, is:
P(k) = (n choose k) * (p^k) * ((1 - p)^(n - k))
In this case, the probability of a child being a boy (success) is 1/2 (since they are equally likely to be boys or girls), and the probability of a child being a girl is also 1/2.
Using the formula, we can calculate:
P(3 boys and 1 girl) = (4 choose 3) * (1/2)^3 * (1/2)^(4 - 3)
= 4 * (1/2)^3 * (1/2)
= 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.
To determine the probability that a family of four children contains three boys and one girl, we need to calculate the number of possible outcomes that satisfy this condition and divide it by the total number of possible outcomes.
The total number of possible outcomes for each child is two (boy or girl), and since there are four children, the total number of possible outcomes as a whole is:
2 * 2 * 2 * 2 = 2^4 = 16.
To calculate the number of outcomes where there are three boys and one girl, we can use combinations. The number of ways to choose three boys out of four is C(4,3) = 4 (as there are four ways to choose three boys). For the remaining child, there is only one choice, which is a girl. Therefore, the number of outcomes with three boys and one girl is:
4 * 1 = 4.
So the probability that a family of four children contains three boys and one girl is:
(Outcomes with three boys and one girl) / (Total number of outcomes) = 4 / 16 = 1/4.
Therefore, the probability is 1/4 or 0.25.
To find the probability of a family of four children containing three boys and one girl, we need to consider all the possible outcomes and determine the favorable outcomes.
The number of outcomes in this scenario is given by the combination formula. Since there are four children and each child can be either a boy or a girl, there are 2 possibilities for each child, yielding a total of 2^4 = 16 possible outcomes.
To determine the number of favorable outcomes where there are three boys and one girl, we can use the combination formula again. We want to choose three positions out of the four positions to be filled with boys, and the remaining position will be filled with a girl. The number of ways to choose three out of four is given by the combination formula (4 choose 3), which is equal to 4.
Therefore, the number of favorable outcomes is 4.
The probability is then calculated by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 4 / 16
Probability = 1 / 4
So, the probability that a family of four children contains three boys and one girl is 1/4 or 25%.