Question

sweepstakes sweep [12 points] 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 has entered the contest?

Answer 1

The probability that Kumar, Janice, and Pedro each win a prize in a sweepstakes is approximately 0.0000000103 or 1.03 * 10^-8.

Step-by-step explanation:

To find the probability that Kumar, Janice, and Pedro each win a prize in a sweepstakes, we need to consider the total number of possible outcomes and the number of favorable outcomes. Since there are 100 people entering the contest and each winner is selected at random for first, second, and third prizes, we can calculate the probability as:

1. The probability that Kumar wins a prize is 1 out of 100 (1/100).
2. After Kumar wins a prize, the probability that Janice wins a prize is 1 out of 99 (1/99) since there are now only 99 people remaining.
3. After Kumar and Janice win prizes, the probability that Pedro wins a prize is 1 out of 98 (1/98) since there are now only 98 people remaining.

To find the overall probability, we multiply the individual probabilities:

Probability(Kumar, Janice, and Pedro each win a prize) = Probability(Kumar wins) imes Probability(Janice wins after Kumar) imes Probability(Pedro wins after Kumar and Janice)

Probability(Kumar, Janice, and Pedro each win a prize) = (1/100) imes (1/99) imes (1/98)

Using a calculator or software, the answer is approximately 0.0000000103 or 1.03 * 10-8.