Question

The 8 acts for a talent show are being ordered randomly. What is the probability that the dance group is first followed by the comedian?

Answer 1

The specified event consists of two events that must occur one after the other:

1. A dance group must be selected from eight participants. The probability of this event:

$P_1=1/8.$

2. A comedian must be selected from the seven remaining participants. The probability of this event

$P_2=1/7.$

The required probability value is equal to the product of the probabilities of these two events:

$P=P_1\cdot P_2=\frac{1}{8}\cdot \frac{1}{7}=0.018.$

Answer: 0.018 or 1.8 %.