Question

You are playing the duck pond game at the carnival! There are 20 ducks in the pond. Five of the ducks have blue dots on their bellies. You win if you pick up a duck that has a blue dot. You can play one round for $1 or four rounds for $3. In each round you will pick a duck out of the pond and see if it has a blue dot on its belly. If you win you get a prize. After that you place the duck back in the pond, close your eyes, and the worker moves all of the ducks around. If you play the duck pond game four times, what is the probability that you will win three of the times? (Hint: How many possible outcomes are there for this experiment?)

Answer 1

Answer: Pt= 3/256

Step-by-step explanation:

For each round the probability of winning is:

Pw = number of blue dotted ducks/ total number of ducks

Pw= 5/20 ( since the duck is being replaced)

The probability of losing is:

Pl= number of ducks without blue dotted belly/ total number of ducks

Pl = 15/20

Therefore the probability of winning 3 times out of 4 is:

Pt= Pw× Pw×Pw×Pl

Pt= (5×5×5×15)/(20×20×20×20)

Pt= 1875/160000

Pt= 3/256

Goodluck...