It is assume that when she children are born they are equally likely to be boys or girls what is the probability that a family contain four children conthree boys and one girl
Based on the assumption that the probability of having a boy or a girl is the same, we can use the concept of binomial probability to calculate the probability of a family having three boys and one girl among four children.
The binomial probability formula is P(x) = (nCx) * (p^x) * ((1-p)^(n-x)), where:
- P(x) is the probability of getting exactly x successes in n trials
- n is the number of trials or children in this case (4)
- x is the desired number of successes or boys in this case (3)
- p is the probability of success or having a boy in this case (0.5)
- (nCx) is the combination formula (n! / (x! * (n-x)!))
Using this formula:
P(3 boys and 1 girl) = (4C3) * (0.5^3) * (0.5^(4-3))
= (4!/((3!)(4-3)!)) * (0.5^3) * (0.5)
= (4/((3!)(1!))) * (0.5^3) * 0.5
= (4) * (0.125) * 0.5
= 0.25
Therefore, the probability that a family with four children contains three boys and one girl is 0.25 or 25%.
To find the probability that a family contains four children with three boys and one girl, we can use the concept of binomial probability.
The probability of having a boy or a girl is equal, which means the probability of having a boy is 1/2, and the probability of having a girl is also 1/2.
In this case, we want to find the probability of having exactly three boys (successes) in a family of four children. This can be calculated using the binomial probability formula:
P(X=k) = (nCk) * p^k * q^(n-k)
Where:
P(X=k) is the probability of having exactly k successes (in this case, boys).
n is the total number of trials (in this case, the total number of children).
k is the desired number of successes (in this case, 3 boys).
p is the probability of success (in this case, the probability of having a boy, 1/2).
q is the probability of failure (in this case, the probability of having a girl, also 1/2).
nCk is the binomial coefficient, which represents the number of possible combinations of k successes out of n trials.
Using the values we have, we can substitute them into the formula:
P(X=3) = (4C3) * (1/2)^3 * (1/2)^(4-3)
Calculating the values:
(4C3) = 4! / (3!(4-3)!) = 4
(1/2)^3 = 1/8
(1/2)^(4-3) = 1/2
Plugging the values into the formula:
P(X=3) = 4 * 1/8 * 1/2
= 4/16
= 1/4
Therefore, the probability that a family contains four children, with three boys and one girl, is 1/4 or 25%.
To find the probability that a family with four children contains three boys and one girl, we need to consider all the different outcomes that satisfy this condition.
In this scenario, we are assuming that each child is equally likely to be a boy or a girl. Therefore, the possible outcomes for each child are: B (boy) or G (girl).
Now, to calculate the probability, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Let's go step by step:
Step 1: Find the number of favorable outcomes (families with three boys and one girl).
To have three boys and one girl, we can consider the order in which the children are born.
Possible favorable outcomes:
- B B B G
- B B G B
- B G B B
- G B B B
Note that each outcome represents one child's gender, and the order matters because the gender of each child is different.
Step 2: Find the total number of possible outcomes (all the families that can be formed).
Since there are two equally likely possibilities for each child (boy or girl), and we have four children, the total number of possible outcomes is 2^4 = 16.
Each child has two choices (boy or girl), and for four children, we need to multiply 2 by itself four times (2^4).
Step 3: Calculate the probability.
Now that we have the number of favorable outcomes (4) and the total number of possible outcomes (16), we can calculate the probability.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 16
Probability = 1 / 4
Probability = 0.25
Therefore, the probability that a family with four children contains three boys and one girl is 0.25, or 25%.