please help me with this probability word problem .

Question

An urn contains pink and green balls. Four balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all balls drawn from the urn are green? Round your answer to three decimal places.

 

thank you for all the help in advance!!!!

Answer 1

The probability of picking a single green ball is:

 

     P(green) = (number of green balls in the urn)/(total number of balls in the urn)

 

So if there are 8 green balls in the urn and 16 pink balls:

 

     P(green) = 8/(8+16) = 8/24 = 1/3

 

If you put the ball back after each pick, then P(green) doesn't change because there are still 8 green balls in the urn and 24 total balls.  The probability of picking 4 green balls with replacement  is:

 

P(4 green) = P(green) * P(green) * P(green) *P(green)  

P(4 green) = 1/3 * 1/3 * 1/3 * 1/3 = _____

 

Look up the number of green and pink balls stated in the problem and use those numbers (rather than the one I made up of 8 green and 16 pink balls) to solve the problem for yourself.