The 19th-20th Century mathematician and philosopher Alfred North Whitehead has b

Question

The 19th-20th Century mathematician and philosopher Alfred North Whitehead has been quoted as saying "The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit. Another claimant for this position is music." Are those creative in mathematics also creative in music and conversely are those creative in music also creative in math. Suppose that 29% of all students are creative in music. Suppose 30% of those students creative in music are also creative in math. In addition, suppose that 15% of students not creative in music are creative in math. Suppose we randomly select a student. Let U be the event the student is creative in music. Let M be the event the student is creative in math.

a. Calculate P(M), i.e the probability the student is creative in math?   
b. Calculate P(M U), i.e. the probability the student is creative in math and music.  
c. Calculate the probability that the student is creative in music given that the student is creative in math. i.e. P(U|M)  
d.If we independently select 5 students then what is the probability that they are all creative in music?  
e.If we independently select 5 students then what is the probability that none of them are creative in music?

Explanation / Answer

from abvoe information:

P(U) =0.29 ; P(M|U) =0.30 ; P(M|Uc) =0.15

a) P(M) =P(U)*P(M|U)+P(Uc)*P(M|Uc) =0.29*0.3+(1-0.29)*0.15 =0.1935

b)

P(M n U) =P(U)*P(M|U) =0.29*0.3 =0.087

c) P(U|M) =P(M n U)/P(M) =0.087/0.1935 =0.4496

d) probability that they are all creative in music =(0.29)5 =0.0021

e) probability that none of them are creative in music =(1-0.29)5 =0.1804

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