Suppose you have a big vat of balls and that 70% of the balls are green and 30% of the balls are red. Suppose you randomly select a ball, record the color, then put the ball back, and repeat the process.
(a) What is the probability that the first red ball you encounter will be the third ball you pull from the vat? Clearly state which probability distribution's PMF you are using to perform this calculation as well as which value is to be given to each variable in the PMF. Then compute the answer to the question.
(b) What is the probability that the sixth ball you pull from the vat is the third time you pulled a green ball? Clearly state which probability distribution's PMF you are using to perform this calculation as well as which value is given to each variable in the PMF. Then compute the answer to the question.
(c) What is the probability that after pulling 6 balls, you have pulled exactly three green balls? Clearly state which probability distribution's PMF you are using to perform this calculation as well as which value is given to each variable in the PMF. Then compute the answer to the question.