Respuesta :
Answer:
Probability of any event is defined by
[tex]P(E)=\frac{favourable case}{Total cases}[/tex]
a)
Since any of the six comedians can perform first so the probability that comic D will perform first is given by [tex]\frac{1}{6}[/tex]
b)
The probability of event that comic C will perform first and comic E will perform fourth is given by
[tex]P(E_{2})=P_{1}\times P_{2}\\\\P(E_{2})=\frac{1}{6}\times \frac{1}{5}=\frac{1}{30}[/tex]
c)
The no of ways the comics can perform are all the possible arrangements of 6 comics which are equal to [tex]6!=720[/tex]
Out of these arrangements only one will correspond to the order of D,C,E,A,B,F thus the probability becomes
[tex]P(E_{3})=\frac{1}{720}[/tex]
d)
The probability that comic B or comic F will perform third is given by
[tex]P(E_{4})=P_{1}+P_{2}\\\\P(E_{4})=\frac{1}{6}+\frac{1}{6}=\frac{1}{3}[/tex]
where [tex]P_{1}[/tex] is the probability that comic B will perform third and
[tex]P_{2}[/tex] is the probability that comic F will perform third
