Answer:
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
