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? )

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...

The two events are independent because having brown eyes does not depend on being male or female.

Step-by-step explanation:

Dependent & Independent Variables relationship show the cause effect relationship between two variables.

Independent Variable is the variable which is the causal variable, leading to effect in Dependent Variable. Dependent Variable is the variable being effected by Dependent Variable.

Person's eye colour & his / her sex (male or female) are not related to each other. Brown colour eyes don't depend on a person being male or female. So, these variables are un-related to each other, or - independent of each other.