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Chapter 4: Problem 85

The probability that a student graduating from Suburban State University has student loans to pay off after graduation is .60. If two students are randomly selected from this university, what is the probability that neither of them has student loans to pay off after graduation?

Short Answer

Expert verified
The probability that neither of the two randomly selected students from Suburban State University has student loans to pay off after graduation is 0.16.

Step by step solution

01

Identify the probability of one student not having a loan

The problem states that the probability that a student has a loan is 0.60, thus the probability \(P(A')\) that a student does not have a loan can be calculated using the formula \(P(A') = 1 - P(A)\). In this case, \(P(A) = 0.60\), thus \(P(A') = 1 - 0.60 = 0.40\). This means that the probability of one student not having a loan is 0.40.
02

Calculate the combined probability

Given that these are independent events, the combined probability of two independent events, or the probability that both students do not have a loan, can be calculated by multiplying their individual probabilities together. This is represented as \(P(A' \cap B') = P(A') \cdot P(B')\). In this case, as both events (A and B) indicate a student not having a loan, their probabilities are the same: \(P(A') = P(B') = 0.40\). Therefore, the combined probability is \(P(A' \cap B') = 0.40 \cdot 0.40 = 0.16\).

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Most popular questions from this chapter

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