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.

Answer:A. 0.1B. 0.8C. 0.5Step-by-step explanation:Given:P(Science) = 0.3P(Arts) = 0.6P(none) = 0.2From 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 degreeLet P(Arts and Science) = the probability that a student gets a Bachelor of Arts degree and Bachelor of Science degreeFor independent events,P(A) + P(B) - P(A and B) + P(none)= 1If we translate the above formula to suit our needs, we have something like thisP(Science) + P(Arts) - P(Arts and Science) + P(none) = 1OrP(Arts) + P(Science) - P(Arts and Science) + P(none) = 1From this, we have0.3 + 0.6 - P(Arts and Science) + 0.2 = 11.1 - P(Arts and Science) = 1-P(Arts and Science) = 1 - 1.1-P(Arts and Science) = -0.1P(Arts and Science) = 0.1B. The probability that a student gets a Bachelor of Science or Bachelor of Arts degreeFor independent eventsP(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 - 0.1P(Arts or Science) = 0.8C. The probability that a student gets only Bachelor of ArtsP(A only) = P(A) - P(A and B)P(Arts) = P(Arts) - P(Arts and Science)P(Arts) = 0.6 - 0.1P(Arts) = 0.5