Exam P Practice Problem 85 – Supplemental Coverages for Employees

Problem 85-A

A large employer offers three supplemental benefits in addition to the major medical benefit – dental, vision and group life insurance – to its employees. The following information is known.

  • Thirty five percent of the employees choose dental and vision.
  • Twelve percent of the employees choose all three supplemental benefits.
  • Fifty six percent of the employees choose exactly two of the three supplemental benefits.
  • Sixteen percent of the employees choose neither vision nor dental.
  • Five percent of the employees choose none of the three supplemental benefits.

One employee is chosen at random. What is the probability that this employee has group life insurance benefit?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.32

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.56

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.63

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.65

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.68

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Problem 85-B

A professor tracks a group of students taking astrophysics, biostatistics and chemistry. The following information is known.

  • Forty five percent of the students pass astrophysics and biostatistics.
  • Nineteen percent of the students pass biostatistics and chemistry only.
  • Twenty two percent of the students pass neither biostatistics nor chemistry.
  • Sixty seven percent of the students pass biostatistics.
  • Thirty four percent of the students pass astrophysics and biostatistics only.

One student is chosen at random. What is the probability that this student passes chemistry?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.35

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.40

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.41

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.47

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.53

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Answers

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\copyright \ 2014 \ \ \text{ Dan Ma}

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2 responses

  1. Hello Dan, for question 85-B, it seems that there is a error, because the number of student who pass biostatistics (62) is less than the number of student who pass Astrophysics and Biostatistics (45) + only biostatistics and chemistry (19).
    Could you explain how can i resolve this question
    Thanks

    1. Hi, Wen

      Thanks for pointing out the error. The error for 85-B has been fixed. The problem can now be solved.

      Dan Ma

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