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