Question

Six​ stand-up comics,​ A, B,​ C, D,​ E, and​ F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. Find the probability​ that: a. Comic D will perform first. b. Comic C will perform first and Comic E will perform fourth. c. The comedians will perform in the following​ order: D, C, E, A, B, F. d. Comic B or Comic F will perform third.

Answer 1

Answer:

Probability of any event is defined by

$P(E)=\frac{favourable case}{Total cases}$

a)

Since any of the six comedians can perform first so the probability that comic D will perform first is given by $\frac{1}{6}$

b)

The probability of event that comic C will perform first and comic E will perform fourth is given by

$P(E_{2})=P_{1}\times P_{2}\\\\P(E_{2})=\frac{1}{6}\times \frac{1}{5}=\frac{1}{30}$

c)

The no of ways the comics can perform are all the possible arrangements of 6 comics which are equal to $6!=720$

Out of these arrangements only one will correspond to the order of D,C,E,A,B,F  thus the probability becomes

$P(E_{3})=\frac{1}{720}$

d)

The probability that comic B or comic F will perform third is given by

$P(E_{4})=P_{1}+P_{2}\\\\P(E_{4})=\frac{1}{6}+\frac{1}{6}=\frac{1}{3}$

where $P_{1}$ is the probability that comic B will perform third and

$P_{2}$ is the probability that comic F will perform third