University degree requirements typically are different for bachelor of science degrees and bachelor of arts degrees. some students get a bachelor of arts and science degree, which requires meeting graduation criteria for both degrees. a student advisor needs to know the probability a newly admitted student is interested in such a program, so that the student can be properly advised. a study of previous years finds that the probability a student gets a bachelor of science degree is p(science)=0.3 and the probability a student gets a bachelor of arts degree is p(arts)=0.6 . the study also shows that the probability a student gets no degree is p(no)=0.2 .
a - the probability a student gets a bachelor of arts and science degree is:
a) 0.3.
b) 0.6.
c) 0.1.
d) 0.2.
b - the probability a student gets a bachelor of arts degree or a bachelor of science degree is:
a)0.9.
b) 0.3.
c) 0.6.
d) 0.8.
c - the probability a student gets only a bachelor of arts degree is:
a) 0.1.
b) 0.5.
c) 0.3.
d) 0.6.

A. 0.1

B. 0.8

C. 0.5

Step-by-step explanation:

Given:

P(Science) = 0.3

P(Arts) = 0.6

P(none) = 0.2

From the above, it is understood that the events are independently events; meaning that the probability that a students gets a Bachelor of Science degree does not affect the probability of the same student getting a Bachelor of Arts degree.

A. The probability that a student gets a Bachelor of Science and Bachelor of Arts degree

Let P(Arts and Science) = the probability that a student gets a Bachelor of Arts degree and Bachelor of Science degree

For independent events,

P(A) + P(B) - P(A and B) + P(none)= 1

If we translate the above formula to suit our needs, we have something like this

P(Science) + P(Arts) - P(Arts and Science) + P(none) = 1

Or

P(Arts) + P(Science) - P(Arts and Science) + P(none) = 1

From this, we have

0.3 + 0.6 - P(Arts and Science) + 0.2 = 1

1.1 - P(Arts and Science) = 1

-P(Arts and Science) = 1 - 1.1

-P(Arts and Science) = -0.1

P(Arts and Science) = 0.1

B. The probability that a student gets a Bachelor of Science or Bachelor of Arts degree

For independent events

P(A or B) = P(A) + P(B) - P(A and B)

So, P(Arts or Science) = P(Arts) + P(Science) - P(Arts and Science)

P(Arts or Science) = 0.3 + 0.6 - 0.1

P(Arts or Science) = 0.8

C. The probability that a student gets only Bachelor of Arts

P(A only) = P(A) - P(A and B)

P(Arts) = P(Arts) - P(Arts and Science)

P(Arts) = 0.6 - 0.1

P(Arts) = 0.5

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step-by-step explanation:

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