Pregunta
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The probability that a randomly selected person in Newfoundland has a university degree is \( 23 \% \). The probability that a randomly selected person in Newfoundland has a college diploma is \( 16 \% .1 \% \) of the population has both a university degree and a college diploma. What is the probability that a randomly selected individual in Newfoundland has either a university degree or a college diploma? Enter your numerical answer in the space provided below, and in the Units box place the percent (\%) symbol. Your Answer:

Ask by Wells Estrada. in Canada
Feb 26,2025

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The probability is 38%.

Solución

Let U be the event of having a university degree, and C be the event of having a college diploma. Given: • P(U) = 23% • P(C) = 16% • P(U ∩ C) = 1% To find the probability of having either a university degree or a college diploma, we use the formula: P(U ∪ C) = P(U) + P(C) − P(U ∩ C) Plugging in the values: P(U ∪ C) = 23% + 16% − 1% = 38% Thus, the probability that a randomly selected individual in Newfoundland has either a university degree or a college diploma is 38%.

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The Deep Dive

To find the probability that a randomly selected individual in Newfoundland has either a university degree or a college diploma, we can use the formula for the union of two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Here: - \(P(A)\) = probability of a university degree = \(23\% = 0.23\) - \(P(B)\) = probability of a college diploma = \(16\% = 0.16\) - \(P(A \cap B)\) = probability of both a university degree and a college diploma = \(0.1\% = 0.001\) Now, substituting the values into the formula: \[ P(A \cup B) = 0.23 + 0.16 - 0.001 = 0.388 \] To express this as a percentage, we multiply by 100: \[ P(A \cup B) = 0.388 \times 100 = 38.8\% \] So, your numerical answer is: **38.8%**.

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