# Conditional Probability of children

• succubus
In summary, the question is asking for the conditional probability of a family having 1 or 4 children, given that the randomly chosen child is the eldest in the family. The events are independent, so the probability of having 4 children is simply .3. The probability of having 1 child is .1. To calculate the conditional probability, the probability of having 4 children (.3) is multiplied by 1/4 (since there are 4 children to choose from in the family) and then divided by the probability of the eldest child being chosen (P(E)). Therefore, the conditional probability for a) is 1/4 and for b) it is .3/P(E).
succubus
This is probably relatively easy, but I'm still a bit confused...

The question:

A family has j children with probability p1 = .1, p2 = .25, p3 = .35, p4 = .3.
A child is randomly chosen. Given this child is the eldest in the family, find the conditional probability that
a) Family has 1 child
b) Family has 4 children

A is easy (1), so let's move to b.

I have the following setup

E = event child is eldest
F = event family has 4 children

P(E) = (1*.1) + (.5 * .25) + (.3333 * .35) + (.25 * .3)

And

P(F) = .3

So the set up should be P(F|E) = .25*P(E)/P(E) ??

The events are independent correct? So I probably shouldn't include the ratio of how many children there are to choose from multiplied by the probability??

I'm kind of anxious and worried. Got 3 tests to study for an am sick. So I apologize if it's too easy :)

These problems tend to make my head hurt. And hence give wrong answers. But isn't the pool of children to select from only the oldest members of each family, given your given? If a) then reads 'at least one child', then sure. Probability 1. If a) reads 'exactly one child' isn't it just .1. Likewise for b) isn't it just .3? I may be more confused than enlightening here. Perhaps I don't understand the problem.

I think I figured it out. I think it's the probability of having 4 children (.3) times 1/4 divided by P(E) where
P(F|E) = .25 * .30
P(E) = 1*.1 + 1/2*.25 + 1/3*.35 + 1/4*.3

P(F|E) / P(E) ?

Does this seem right?

## What is conditional probability of children?

Conditional probability of children refers to the likelihood of a certain event occurring (such as having a child with a certain characteristic or condition) given certain conditions or factors (such as parental genetics or environmental factors).

## How is conditional probability of children calculated?

Conditional probability of children is calculated by dividing the probability of the event occurring under specific conditions by the overall probability of the event occurring regardless of conditions. This can be represented as P(A|B) = P(A and B)/P(B), where A represents the event and B represents the conditions.

## What factors influence the conditional probability of children?

The conditional probability of children can be influenced by a variety of factors such as genetics, environmental factors, lifestyle choices, and medical history. Additionally, the probability may also be affected by the presence of other conditions or characteristics in the child's parents or family members.

## How is conditional probability of children used in research?

Conditional probability of children is often used in research to understand the likelihood of certain genetic or environmental factors contributing to the occurrence of a specific condition or characteristic in children. This can help researchers identify potential risk factors and develop interventions or treatments.

## What are some limitations of using conditional probability of children?

One limitation of using conditional probability of children is that it does not necessarily prove causation. Just because there is a high probability of a certain event occurring under specific conditions does not mean that those conditions caused the event to occur. Additionally, factors such as sample size and bias can also impact the accuracy of conditional probability calculations.

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