The prerequisite for a required course is that students must

The prerequisite for a required course is that students must have taken either course A or course B. By the time they are juniors, 57% of the students have taken course A, 29% have had course B, and 14% have done both.

a) What percent of the juniors are ineligible for the course?

b) What\'s the probability that a junior who has taken course A has also taken course B?

a)___ of juniors are not eligible.

b) The probability that a junior who has taken course A has also taken course B is ___

Solution

Solution:

P(A) = 0.57, students have taken course? A
P(B) = 0.29 , course? B
P(A ? B) = 0.14 , have done both courses

percent of the juniors are ineligible for the? course?=

=1 - P(A ? B)

=1-[P(A)+P(B)-P(A ? B]

=1-[057+0.29-0.14]

= 1-0.72 =0.28

percent of the juniors are ineligible for the? course =28%

(b)

Probability of A given B is P(B | A) = P(B ? A) / P(A) =0.14/0.57= 0.246

   =24.6%

_28%__ of juniors are not eligible.

The probability that a junior who has taken course A has also taken course B is24.6%