Question

About 53% of the students are females. A random sample with five students were selected.

A. What is the probability that there is only one male student in this sample?

B. What is the probability that there are two male students in this sample?

C. What is the probability that there are three male students in this sample?

D. What is the probability that there is at least one male student in this sample?

E. Given that there is at least one male student in this sample, what is the probability that there is only one male student in this sample?

F. Given that there is at least one female student in this sample, what is the probability that there is only one female student in this sample?

Answer 1

a)P( only one male student in this sample )=⁵C₁(0.47)¹(0.53)⁴ =0.185426

b) probability that there are two male students in this sample =⁵C₂(0.47)²(0.53)³ =0.328869

c) probability that there are three male students in this sample =P(X=3)=0.291639

d) probability that there is at least one male student in this sample =P(X>=1)=1-P(X=0)=1-0.04182 =0.958180

e) P(X=1|X>=1)=P(X=1)/P(X>=1)=0.185426/0.958180=0.193519

f)P(Y=1|Y>=1)=⁵C₁(0.53)¹(0.47)⁴/(1-047⁵)=0.132347