A magazine reported the following information for Ph.D. degrees awarded by a certain country's colleges in the 2013–2014 academic year. (Round your answers to three decimal places.)
A total of 54,070 Ph.D. degrees were awarded.
12,804 of these degrees were in the life sciences.
10,059 of these degrees were in the physical sciences.
The remaining degrees were in majors other than life or physical sciences.
(a) What is the probability that a randomly selected Ph.D. student who received a degree in 2013–2014 received a degree in the life sciences?
(b) What is the probability that a randomly selected Ph.D. student who received a degree in 2013–2014 received a degree that was not in a life or a physical science?
(c) What is the probability that a randomly selected Ph.D. student who received a degree in 2013–2014 did not receive a degree in the physical sciences?
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(a) The probability that a randomly selected Ph.D. student who received a degree in 2013-2014 received a degree in the life sciences is given by:
P(Life Sciences) = Number of degrees in Life Sciences / Total number of degrees awarded
P(Life Sciences) = 12,804 / 54,070 ≈ 0.236
Therefore, the probability is approximately 0.236.
(b) The probability that a randomly selected Ph.D. student who received a degree in 2013-2014 received a degree that was not in a life or physical science is given by:
P(Other Majors) = Number of degrees in Other Majors / Total number of degrees awarded
To find the number of degrees in Other Majors, we subtract the number of degrees in Life Sciences and Physical Sciences from the total number of degrees awarded:
Number of degrees in Other Majors = Total number of degrees awarded - Number of degrees in Life Sciences - Number of degrees in Physical Sciences
Number of degrees in Other Majors = 54,070 - 12,804 - 10,059 = 31,207
P(Other Majors) = 31,207 / 54,070 ≈ 0.577
Therefore, the probability is approximately 0.577.
(c) The probability that a randomly selected Ph.D. student who received a degree in 2013-2014 did not receive a degree in the physical sciences is given by:
P(Not Physical Sciences) = 1 - P(Physical Sciences)
P(Not Physical Sciences) = 1 - (Number of degrees in Physical Sciences / Total number of degrees awarded)
P(Not Physical Sciences) = 1 - 10,059 / 54,070 ≈ 0.814
Therefore, the probability is approximately 0.814.
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