Many colleges require students to take a placement exam to determine which math courses they are eligible to take during the first semester of their freshman year. Of the 2938 freshmen at a local state college, 254 were required to take a remedial math course, 1478 could take a nonremedial, non-calculus-based math course, and 1206 could take a calculus-based math course.a. If one of the freshmen is selected at random, find the probability that this student could take a calculus-based math course.Round your answer to three decimal places.P(the student taking a calculus-based math course)= Enter you answer; P(the student taking a calculus-based math course) b. If one of the freshmen is selected at random, find the probability that this student could take a nonremedial, non-calculus-based math course.Round your answer to three decimal places.P(the student taking a nonremedial, non-calculus-based math course)= Enter you answer; P(the student taking a nonremedial, non-calculus-based math course) c. If one of the freshmen is selected at random, find the probability that this student could take a remedial math course.Round your answer to three decimal places.P(the student taking a remedial math course)= Enter you answer; P(the student taking a remedial math course) Should these probabilities add up to 1.0?Choose your answer; Should these probabilities add up to 1.0?eTextbook and MediaAttempts: 0 of 5 used

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JaserF631280 JaserF631280

28-10-2022
Mathematics

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Many colleges require students to take a placement exam to determine which math courses they are eligible to take during the first semester of their freshman year. Of the 2938 freshmen at a local state college, 254 were required to take a remedial math course, 1478 could take a nonremedial, non-calculus-based math course, and 1206 could take a calculus-based math course.a. If one of the freshmen is selected at random, find the probability that this student could take a calculus-based math course.Round your answer to three decimal places.P(the student taking a calculus-based math course)= Enter you answer; P(the student taking a calculus-based math course) b. If one of the freshmen is selected at random, find the probability that this student could take a nonremedial, non-calculus-based math course.Round your answer to three decimal places.P(the student taking a nonremedial, non-calculus-based math course)= Enter you answer; P(the student taking a nonremedial, non-calculus-based math course) c. If one of the freshmen is selected at random, find the probability that this student could take a remedial math course.Round your answer to three decimal places.P(the student taking a remedial math course)= Enter you answer; P(the student taking a remedial math course) Should these probabilities add up to 1.0?Choose your answer; Should these probabilities add up to 1.0?eTextbook and MediaAttempts: 0 of 5 used

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CharlynnY330710 CharlynnY330710 · Answer 1 · 2022-10-28T12:30:23+02:00

Given:

Total number of students = 2938

Number of remedial math course students = 254

Number of nonremedial math course students = 1478

Number of calculus-based math = 1206

Required:

(1) Find the probability that this student could take a calculus-based math course.

(2) Find the probability that this student could take a nonremedial, non-calculus-based math course.

(3) find the probability that this student could take a remedial math course.

Explanation:

The probability formula for an event is given as:

[tex]P=\frac{Number\text{ of possible outcomes}}{Total\text{ number of outcomes}}[/tex]

(1) The probability that this student could take a calculus-based math course.

[tex]\begin{gathered} P(calculus)=\frac{1206}{2938} \\ P(calculus)=0.410 \end{gathered}[/tex]

(2) The probability that this student could take a nonremedial, non-calculus-based math course.

[tex]\begin{gathered} P(nonremedial)=\frac{1478}{2938} \\ P(nonremedial)=0.503 \end{gathered}[/tex]

(3) the probability that this student could take a remedial math course.

[tex]\begin{gathered} P(remedial)=\frac{254}{2938} \\ P(remedial)=0.086 \end{gathered}[/tex][tex]\begin{gathered} P(remedial)=\frac{254}{2938} \\ P(remedial)=0.086 \end{gathered}[/tex][tex]\begin{gathered} P(calculus)+P(nonremedial)+P(remedial)=0.410+0.503+0.086 \\ P(calculus)+P(nonremedial)+P(remedial)=0.999 \\ P(calculus)+P(nonremedial)+P(remedial)\approx1 \end{gathered}[/tex]

Final answer:

[tex]\begin{gathered} P(calculus)=0.410 \\ P(nonremedial)=0.503 \\ P(remedial)=0.086 \\ P(calculus)+P(nonremed\imaginaryI al)+P(remed\imaginaryI al)\approx1 \end{gathered}[/tex]