2 Probability for Business Free Online FlashCards

What range can a probability take?

Probability quantifies uncertainty on a scale from $0$ $impossible$ to $1$ $certain$.

How do you find the probability of not $A$?

The complement of $A$, meaning “not $A$,” has probability $P(A^c)=1-P(A)$.

If $P(E)=0.12$, $P(R)=0.08$, and $P(E\cap R)=0.03$, what is $P(E\cup R)$?

The probability is $0.12+0.08-0.03=0.17$, or 17% of orders.

How is $P(A\mid B)$ defined?

For $P(B)>0$, conditional probability is $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$. It focuses on cases where $B$ occurred.

What is the multiplication rule for two events?

The multiplication rule is $P(A\cap B)=P(A\mid B)P(B)$. Applied successively, it also gives joint probabilities for several events without requiring independence.

What does it mean for two events to be independent?

Events are independent when knowing one occurred does not change the probability of the other. Equivalently, $P(A\mid B)=P(A)$ when defined, or $P(A\cap B)=P(A)P(B)$.

What risk can a shared outage create for two payment processors?

If failures are independent, the probability both processors fail is $0.02\times0.03=0.0006$, or 0.06%. A shared cause can make them dependent and make this product underestimate risk.

What should a business consider before using probabilities to choose a plan?

Define the event, identify relevant conditions, choose a suitable rule, and state assumptions. Probabilities help compare plans but do not determine the best choice without considering consequences and objectives.

What is an event in probability?

An event is an outcome or group of outcomes, such as a customer placing an order or a shipment arriving late.

How do you calculate the probability that $A$ or $B$ occurs?

Use $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Subtract the overlap so outcomes in both events are not counted twice.

How does the addition rule simplify for mutually exclusive events?

If $A$ and $B$ cannot occur together, then $P(A\cap B)=0$, so $P(A\cup B)=P(A)+P(B)$.

Given the order example, what fraction of express orders were returned?

$P(R\mid E)=\frac{0.03}{0.12}=0.25$. Thus, 25% of express orders were returned.