You Explain It! Independence Suppose a mother already has three girls from three separate pregnancies. Does the fact that the mother already has three girls affect the likelihood of having a fourth girl? Explain.

Verified step by step guidance

1. Understand the concept of independence in probability: Two events are independent if the occurrence of one does not affect the probability of the other.
2. Recognize that the gender of each child is generally considered an independent event, assuming no biological or external factors influence the outcome.
3. Recall that the probability of having a girl or a boy in each pregnancy is typically about 0.5 (or 50%), regardless of previous outcomes.
4. Therefore, the fact that the mother already has three girls does not change the probability of having a fourth girl; the chance remains the same as any single pregnancy.
5. Conclude that the events (each child's gender) are independent, so previous results do not affect future probabilities.

Key Concepts

Independence of Events

Independence means the outcome of one event does not influence the outcome of another. In this context, the gender of each child is considered independent, so previous births do not affect future ones.

Probability of Gender at Birth

The probability of having a boy or a girl is generally assumed to be about 50% each time, regardless of previous outcomes. This means each birth is a separate event with equal likelihood for either gender.

Misconception of the Gambler’s Fallacy

The gambler’s fallacy is the mistaken belief that past independent events affect future probabilities. Here, thinking three girls increase or decrease the chance of a fourth girl is an example of this fallacy.