The Smith family has 4 children that are all girls. What is the probability that the next one will be a girl?
You plan on having four children and you want all boys. If you have children, what is the probability you will get four boys?
The prob. that the Smith family's next child will be girl is simply 1/2
In all families with four children the prob that the four children will be all boys is (1/2)^4 = 1/16
Here is a principle involved.
http://www.members.cox.net/dagershaw/lol/Odds.html
I hope this helps a little more. Thanks for asking.
The probability of having a girl or a boy in any given pregnancy is 1/2 or 50%.
In the case of the Smith family, the probability of having another girl after already having four girls is also 1/2 or 50%. Each child's gender is statistically independent of the previous ones, so the probability remains the same for each pregnancy.
For your scenario, the probability of having a boy or a girl in any given pregnancy is again 1/2 or 50%. The probability of having four boys in a row is calculated by multiplying the probabilities of having a boy in each of the four pregnancies:
(1/2) * (1/2) * (1/2) * (1/2) = 1/16 or 6.25%
So, the probability of you having four boys is 1/16 or 6.25%.
To determine the probability of the next child being a girl in the Smith family, we first need to understand the concept of probability.
Probability is calculated by dividing the favorable outcomes by the total possible outcomes. In this case, the favorable outcome is having a girl, and the total possible outcome is either having a boy or having a girl.
For the Smith family, they already have four children, and all of them are girls. So, the favorable outcome is having a girl, and the total possible outcome is having either a boy or a girl.
The probability of having a girl is therefore 1 (the favorable outcome) divided by 2 (the total possible outcome). This simplifies to 1/2 or 0.5, meaning there is a 50% chance that the next child in the Smith family will be a girl.
Now let's move on to the second question about having four boys in your family.
Again, we need to calculate the probability of having four boys out of four children. This can be done by multiplying the probability of having a boy in each individual case.
Assuming that the probability of having a boy is also 1/2 (since each child has an equal chance of being a boy or a girl), we can calculate the overall probability.
The probability of having four boys is (1/2) * (1/2) * (1/2) * (1/2), which simplifies to 1/16 or approximately 0.0625. This means there is only a 6.25% chance of having four boys in a family.