Question
1. A jar contains five blue balls and five red balls. You roll a fair die once. Next you randomly draw (without replacement) as many balls from the jar as the number of points you have rolled with the die.
(a) What is the probability that all of the balls drawn are blue?
(b) What is the probability that the number of points shown by the die is r given that all of the balls drawn are blue?
(a) What is the probability that all of the balls drawn are blue?
(b) What is the probability that the number of points shown by the die is r given that all of the balls drawn are blue?
Answers
P(n) = 1/6
Clearly, P(6 blues) = 0
P(n blues) = 5*4*3*.../(1*2*...n) = 5Cn
so P(n & n blues) = 5Cn/6 for 0<n<6
Clearly, P(6 blues) = 0
P(n blues) = 5*4*3*.../(1*2*...n) = 5Cn
so P(n & n blues) = 5Cn/6 for 0<n<6
oops. I got the denominator in the wrong order.
P(n) = 5/6 * 4/5 * ... n factors = 5*4*3.../(6*5*4...)
= 5Pn*(6-n)!/6!
P(n) = 5/6 * 4/5 * ... n factors = 5*4*3.../(6*5*4...)
= 5Pn*(6-n)!/6!
Related Questions
A drawer contains six bags numbered 1-6, respectively. Bag i contains i blue balls and 2 green balls...
tori had 20 gumballs in a bag. there were 2 red gum balls, 3 blue gum balls, 5 yellow gum balls, and...
A jar contains 7 red balls, 5 green balls, 4 blue balls, and 3 white balls. A sample of size 7 balls...
In a bag full of small balls, 1/4 of these balls are green, 1/8 are blue, 1/12 are yellow and the re...