What is compound probability?

Answer

Compound probability is the likelihood of two or more independent events happening together. It is calculated by multiplying the probabilities of each independent event occurring. The probability of event A and event B both happening equals the probability of A multiplied by the probability of B.

Compound probability applies to mutually exclusive events (events that cannot happen at the same time) and mutually inclusive events (events that can happen together). Each type uses a specific formula for calculation. Compound probability values always lie between 0 and 1, representing the chance or likelihood measure within that range.

What are the key characteristics of compound probability?

The key characteristics of compound probability are:

1. It involves multiple events occurring together.
2. The result is always a value between 0 and 1.
3. Different formulas apply depending on event relationships (independent, mutually exclusive, or mutually inclusive).

What is the formula for compound probability with independent events?

The formula for compound probability with independent events is:

$P(A\text{ and }B)=P(A)\times P(B)$

his formula applies when two events are independent, meaning the outcome of one event does not affect the outcome of the other. To use this formula, identify the probability of event A, identify the probability of event B, and multiply these two probabilities together.

A coin flip and a die roll demonstrate this calculation. The probability of flipping heads (event A) is $\frac{1}{2}$. The probability of rolling a 4 (event B) is $\frac{1}{6}$. The probability of both getting heads and rolling a 4 is:

$\frac{1}{2}\times \frac{1}{6}=\frac{1}{12}$

This formula extends to any number of independent events by multiplying the probability of each event.

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