1. ## Probability Question

Suppose that 100 people enter a contest and that different winners are selected at random for first, second and third prizes. What is the probability that kumar, janice and pedro each win a prize if each entered the contest?

Is this correct? 1/100 + 1/99 + 1/98?

2. Hello, vexiked!

Suppose that 100 people enter a contest and that different winners
are selected at random for first, second and third prizes.
What is the probability that Kumar, Janice and Pedro each win a prize?

Is this correct? . $\frac{1}{100} + \frac{1}{99} +\frac{1}{98}$ ? . . . . no

The probability that Kumar wins a prize is: . $\frac{3}{100}$

And the prob. that Janice wins a prize is: . $\frac{2}{99}$

Then the prob. that Pedro wins a prize is: . $\frac{1}{98}$

The probability that all win a prize is: . $\frac{3}{100}\cdot\frac{2}{99}\cdot\frac{1}{98} \;=\;\frac{1}{161,\!700}$

3. Correct.
You can look at it as two groups of people, those three and the other 97.
It's a hypergeometric with (3 choose 3) times (97 choose 0) divided by (100 choose 3).