Questions: Question 1 1 pts Last year at Townsburg High School, 50% of the graduating seniors took the ACT exam, 59% of the graduating seniors took the SAT exam, and 45% of the graduating seniors took both exams. Assume a student is selected at random from the graduating seniors in such a way that any two seniors are equally likely to be selected. Find the probability that the selected student took at least one of the exams. 0.62 0.61

Question 1
1 pts

Last year at Townsburg High School, 50% of the graduating seniors took the ACT exam, 59% of the graduating seniors took the SAT exam, and 45% of the graduating seniors took both exams. Assume a student is selected at random from the graduating seniors in such a way that any two seniors are equally likely to be selected. Find the probability that the selected student took at least one of the exams.
0.62
0.61

Transcript text: Question 1 1 pts Last year at Townsburg High School. 50\% of the graduating seniors took the ACT exam, $59 \%$ of the graduating seniors took the SAT exam, and $45 \%$ of the graduating seniors took both exams. Assume a student is selected at random from the graduating seniors in such a way that any two seniors are equally likely to be selected. Find the probability that the selected student took at least one of the exams. $\qquad$ 0.62 0.61

Solution

Solution Steps

To find the probability that a randomly selected student took at least one of the exams, we can use the principle of inclusion-exclusion. The probability that a student took at least one exam is the sum of the probabilities of taking each exam minus the probability of taking both exams.

Step 1: Identify Given Probabilities

We are given the following probabilities:

Probability of a student taking the ACT exam: $ P(\text{ACT}) = 0.50 $
Probability of a student taking the SAT exam: $ P(\text{SAT}) = 0.59 $
Probability of a student taking both exams: $ P(\text{ACT} \cap \text{SAT}) = 0.45 $

Step 2: Apply the Principle of Inclusion-Exclusion

To find the probability that a student took at least one of the exams, we use the principle of inclusion-exclusion: \[ P(\text{ACT} \cup \text{SAT}) = P(\text{ACT}) + P(\text{SAT}) - P(\text{ACT} \cap \text{SAT}) \]

Step 3: Calculate the Probability

Substitute the given probabilities into the formula: \[ P(\text{ACT} \cup \text{SAT}) = 0.50 + 0.59 - 0.45 = 0.64 \]