Question

1. Of all the students who take the CPA examination, one-fourth have a Master’s degree and the remainder have Bachelor’s degrees. Half of the students with Bachelor’s degrees pass the examination, and three-fourths of those with Master’s degrees pass.

a. Create a joint probability table that represents this information.

b. Find the probability that a student chosen at random from those taking the exam will pass.

c. What is the probability that a student both has a Bachelor’s degree and passes the examination?

d. What is the probability that a student with a Bachelor’s degree will not pass the examination?

e. What is the probability that a student who has not passed the examination has a Master’s degree?

f. What is the probability that a student either passes the examination or has a Bachelor’s degree, or both?

Answer 1

1)a) below is joint probability table :

	pass	did not pass	total
Master’s degree	0.1875	0.0625	0.25
Bachelor’s degrees	0.375	0.375	0.75
total	0.5625	0.4375	1

b)

probability that a student chosen at random from those taking the exam will pass =0.5625

c)

probability that a student both has a Bachelor’s degree and passes the examination =0.375

d)

probability that a student with a Bachelor’s degree will not pass the examination =P(did not pass| Bachelor's degree) =0.375/0.75 =0.5

e)

probability that a student who has not passed the examination has a Master’s degree

=0.0625/0.4375=0.142857

f) probability that a student either passes the examination or has a Bachelor’s degree, or both

=0.5625+0.75-0.375 =0.9375