The probability that kumar, janice, and pedro each win a prize if each has entered the contest is 1/161700.
Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Total number of people,n = 100
Number of people selected in the contest,r = 3
This event can be found by using the combinations concept in probability,
[tex]nC_{r}=\frac{n!}{r!(n-r)!}[/tex]
⇒ [tex]nC_{r}=\frac{100!}{3!(100-3)!}[/tex]
⇒ [tex]nC_{r}=\frac{97!(98)(99)(100)}{6(97)!}[/tex]
⇒ [tex]nC_{r}=\frac{(98)(99)(100)}{6}[/tex]
⇒ [tex]nC_{r}=161700[/tex]
Thus the required probability that kumar, janice, and pedro each win a prize if each has entered the contest is P(E) = [tex]\frac{1}{161700}[/tex]
Hence we can conclude that the probability that kumar, janice, and pedro each win a prize if each has entered the contest is 1/161700.
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