Question

4848​% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

Answer 1

Given the information, we shall proceed as follows:
The given problem is a binomial problem. 
n=10 and p=0.48
thus, the probability that the number who consider themselves baseball fans is:
a] exactly five
P(x=5)=10C5(0.48)^5(0.52)^5=0.244

b] at least 6
P(x>=6)=1-P(x<8)
=P(6)+P(7)+P(8)+P(9)+P(10)
=10C6(0.48)^6(0.52)^4+10C7(0.48)^7(0.52)^3+10C8(0.48)^8(0.52)^2+10C9(0.48)^9(0.52)^1+10C10(0.48)^10
=0.1878+0.0991+0.0343+0.0070+0.0007
=0.3289
The answer: 0.3289

c] Less than 6
P(x<6)=1-P(x>=6)
=1-0.3289
=0.6711