A total of 500 married working couples were polled about...

A total of 500 married working couples were polled about their annual salaries, with the following information resulting: For instance, in 36 of the couples, the wife earned more and the husband earned less than $\$ 25,000 .$ If one of the couples is randomly chosen, what is (a) the probability that the husband earns less than $\$ 25,000 ?$ (b) the conditional probability that the wife earns more than $\$ 25,000$ given that the husband earns more than this amount? (c) the conditional probability that the wife earns more than $\$ 25,000$ given that the husband earns less than this amount?

A total of 500 married working couples were polled about their annual salaries, with the following information resulting:
For instance, in 36 of the couples, the wife earned more and the husband earned less than $\$ 25,000 .$ If one of the couples is randomly chosen, what is
(a) the probability that the husband earns less than $\$ 25,000 ?$
(b) the conditional probability that the wife earns more than $\$ 25,000$ given that the husband earns more than this amount?
(c) the conditional probability that the wife earns more than $\$ 25,000$ given that the husband earns less than this amount?

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Key Concepts

Contingency Table Analysis

Contingency table analysis involves organizing data into a table that displays the frequency distribution of variables, allowing for easier computation of joint, marginal, and conditional probabilities. This method helps in visualizing relationships between categorical variables, such as the different salary categories in each couple.

Conditional Probability

Conditional probability measures the likelihood of an event occurring given that another event has occurred. It is calculated using the formula P(A|B) = P(A ? B) / P(B), where P(A ? B) is the probability of both events happening and P(B) is the probability of the conditioning event. This concept is crucial for understanding how probabilities change when additional information is available.

Probability

Probability is a measure of the likelihood of events occurring, calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes in the sample space. It provides a quantitative description of how likely an event is to occur in a random experiment.

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