Graduation A private college report contains these...

Graduation A private college report contains these statistics: $75 \%$ of incoming freshmen attended public schools. $65 \%$ of public school students who enroll as freshmen eventually graduate. $95 \%$ of other freshmen eventually graduate. a) Is there any evidence that a freshman's chances to graduate may depend upon what kind of high school the student attended? Explain. b) What percent of freshmen eventually graduate?

Graduation A private college report contains these statistics:
$75 \%$ of incoming freshmen attended public schools. $65 \%$ of public school students who enroll as freshmen eventually graduate.
$95 \%$ of other freshmen eventually graduate.
a) Is there any evidence that a freshman's chances to graduate may depend upon what kind of high school the student attended? Explain.
b) What percent of freshmen eventually graduate?

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Key Concepts

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. In the context of the question, it is used to determine the likelihood of a student graduating based on the type of high school they attended.

Law of Total Probability

The law of total probability is a rule that breaks down the probability of an event into several disjoint cases. Here, it is applied in calculating the overall graduation rate by weighting the graduation probabilities of students from different high school backgrounds by their respective proportions.

Weighted Average

A weighted average involves calculating a mean where different values contribute unequally, according to assigned weights. In this problem, the overall freshman graduation rate is computed by taking the weighted average of the graduation chances of students from public schools and from other schools, based on how common each group is among incoming freshmen.

Statistical Dependence

Statistical dependence examines whether the occurrence of one event affects the probability of another event. The problem explores whether a student's graduation chances are influenced by their high school background, indicating a dependency between the type of high school attended and the likelihood of graduating.

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