Question 348023: Hello! I'm just having some trouble with a question on an assignment I have due Monday.
Question: Charlie is 5 years old. He is a very picky eater and can count to 5. His dad makes him a giant bowl of grapes containing only good grapes with the same proportion of red, green, and black grapes. (0.22 Green grapes, 0.24 Black grapes, and 0.54 red grapes. I calculated this in the previous problem.) Charlie randomly picks out 5 grapes from the bowl with replacement after each grape. Charlie will eat one of the grapes that has the majority in 5. If there is a tie, Charlie will not eat a grape in that round. Charlie's dad replaces the grape that has been eaten after each round.
a) Let g be the event of Charlie eating a green grape. Determine the theoretical probability of event g, P(g)
Any help would be appreciated. Thank you so much! :)
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! this is a binomial problem
a picked out grape is green (p(G) = .22) or not green (p(N) = .78)
Charlie must pick out 3 or more green grapes to eat one
you need to sum the first 3 terms of the expansion (p(G) + p(N))^5
5C5{[p(G)]^5} + 5C4{[p(G)]^4}[p(N)] + 5C3{[p(G)]^3}{[p(N)]^2}
|
|
|
