couple plans to have four children what is the probability that three are girls and one is a boy
well each kid is %50 chance.
I want to say that its something like %25 because of the fact that it compounds but don't quote me.
To determine the probability that a couple has three girls and one boy, we can use the binomial probability formula.
The formula for calculating the binomial probability is:
P(X=k) = (n C k) * p^k * q^(n-k)
Where:
- P(X=k) is the probability of exactly k successes (in this case, having exactly 3 girls and 1 boy)
- n is the total number of trials (in this case, 4 children)
- k is the number of successes (in this case, 3 girls)
- p is the probability of a success (in this case, the probability of having a girl)
- q is the probability of a failure (in this case, the probability of having a boy)
Now, let's calculate the probability step-by-step.
Step 1: Calculate the total number of ways to have 3 girls and 1 boy from 4 children.
This can be calculated using the binomial coefficient (n C k) formula, which is the number of ways to choose k items from n distinct items.
In this case, we want to choose 3 girls out of 4 children, so the binomial coefficient is:
(4 C 3) = 4! / (3! * (4-3)!) = 4
Step 2: Calculate the probability of having a girl.
Assuming the probability of having a girl or a boy is equal, the probability of having a girl is 1/2, or 0.5.
Step 3: Calculate the probability of having a boy.
Similarly, the probability of having a boy is also 1/2, or 0.5.
Step 4: Calculate the final probability.
Now, we can plug in the values into the binomial probability formula:
P(X=3) = (4 C 3) * (0.5)^3 * (0.5)^(4-3)
= 4 * 0.5^3 * 0.5^1
= 4 * 0.125 * 0.5
= 0.25
Therefore, the probability that a couple has three girls and one boy is 0.25, or 25%.
To calculate the probability of having three girls and one boy, we need to know the probability of having a girl and a boy at each birth.
Assuming that the probability of having a girl or a boy is equal (50% each), we can use the concept of binomial probability to calculate the probability of a specific outcome. In this case, we want to know the probability of having three girls and one boy.
The binomial probability formula is:
P(x) = (nCx) * p^x * q^(n-x)
Where:
- P(x) is the probability of getting exactly x successes,
- n is the total number of trials or births,
- x is the number of successful births (in this case, the number of girls),
- p is the probability of a single trial being successful (probability of having a girl),
- q is the probability of a single trial being unsuccessful (probability of having a boy).
Now, let's substitute the values into the formula:
n = 4 (total number of births)
x = 3 (number of girls)
p = 0.5 (probability of having a girl)
q = 0.5 (probability of having a boy)
P(3 girls) = (4C3) * (0.5)^3 * (0.5)^(4-3)
To calculate (4C3), which represents the number of combinations of 4 births taken 3 at a time, we use the formula:
(4C3) = 4! / (3! * (4-3)!)
Simplifying this:
(4C3) = 4! / (3! * 1!) = 4
Substituting this value back into the original formula:
P(3 girls) = 4 * (0.5)^3 * (0.5)^(4-3)
= 4 * 0.5^3 * 0.5^1
= 4 * 0.5^4
= 4 * 0.0625
= 0.25
Therefore, the probability of having three girls and one boy in a family of four children, assuming an equal probability of having a girl or a boy, is 0.25 or 25%.