2 Probability for Business Online Quiz Questions

A business assigns an event a probability of $-0.04$. Is this a valid probability?

A company estimates that the probability a shipment arrives late is $(0.18$). What is the probability it does not arrive late?

Two mutually exclusive events have probabilities $(0.24$) and $(0.19$). What is the probability that at least one occurs?

A retailer estimates that $(P(A)=0.35$), $(P(B)=0.40$), and $(P(A\cap B)=0.10$). What is $(P(A\cup B)$)?

A business estimates $(P(A)=0.8$), $(P(B\mid A)=0.5$), and $(P(C\mid A\cap B)=0.25$). What is $(P(A\cap B\cap C)$)? Enter the result as a decimal.

Select all statements that correctly express a test for independence of events $(A$) and $(B$).

Two mutually exclusive events that each have positive probability are independent.

Select all statements that are sound when using a probability model to compare business decisions.

A retailer wants to report the return rate specifically among express orders. Let $(E$) mean an order was express and $(R$) mean it was returned. Which probability represents the requested rate?

Among all deliveries, the probability of both being scheduled for a particular service and arriving damaged is $(0.06$). The probability of being scheduled for that service is $(0.20$). What is the probability that a delivery is damaged given that it was scheduled for that service? Enter the result as a decimal.

For a group of orders, $(P(E)=0.12$) and $(P(R\cap E)=0.03$), where $(E$) means “shipped express” and $(R$) means “returned.” What is the probability that an express order was returned?

A business estimates that two payment processors have failure probabilities $(0.02$) and $(0.03$). An analyst proposes multiplying these values to estimate the probability both fail, but the processors may share a power supply or network. Explain when the product is appropriate, how the shared cause could affect the estimate, and what else the business needs to consider before choosing a plan.

A business estimates that the probability a shipment arrives late is $0.18$. What is the probability that it does not arrive late?

A retailer classifies each transaction as either a cash purchase or a credit purchase, and these categories are mutually exclusive. If the probability of a cash purchase is $0.14$ and the probability of a credit purchase is $0.21$, what is the probability that a transaction is in either category?

In a customer group, the probability of buying product $A$ is $0.30$, the probability of buying product $B$ is $0.20$, and the probability of buying both is $0.08$. What is the probability a customer buys at least one of the two products?

Two mutually exclusive business events each have positive probability. They must be independent because neither event can occur at the same time as the other.

A company finds that $P(A\cap B)=0.09$ and $P(B)=0.30$. What is $P(A\mid B)$? Enter the probability as a decimal.

A business model gives $P(A)=0.20$, $P(B\mid A)=0.50$, and $P(C\mid A\cap B)=0.42$. Using the chain rule, what is $P(A\cap B\cap C)$? Enter the joint probability as a decimal.