Question

Problems 9 and 10 A box contains 2 red balls, 3 white and 1 blue balls. Three balls are selected at random without replacement Find the probability that at most one ballis red. (C) 00.2 01 O 0.6 0.12 0.8 Question 10 2 pts A box contains 2 red balls, 3 white and 1 blue balls. Three balls are selected at random without replacement Find the probability that {at most one ball is red (C) given that at least one ball is red) impossible to calculate from the information given 0.8 0.48 0.75 0.6

Answer 1

A bon contains 2 red balls, 3 white balls and 1 blue ballo. Three balls are selected at random without replacement. To sind the probability that at most one ball is red. Here the process is without replacement, .. The Hypergeometric distribution occurs here. N = Total number of ballo Cice. population gize) : 6 b = sample size = 3 m Parameter in which we interested = 1 red balls = 2 Let, we define the random variables X: getting red balls. 1. x ý Hypergeometric (N-6, M2, D=3) The p.m.is. of hypergeometric distribution is, P(x = x ) :Mc Nam cx co ; X=0,1,2 20=0,1,2,---min (,MJ Ncn o ; otherwise. : P (x<) - P(x=0) + P(x1) 6 - 2 6 - 2 O 6 s9 20 ip(x?i) = 0.8

z) To find the probability that [at most one ball is red] given that cat least one ball is red.) plx & i), x>,1) je p(x<!), P ( x ), 1) =- P ( x (ا, و - = P(x?i).P ( x ,1) - P(x),1) 0.8 l - plxei)] 1 - P[xli] 0.8 [1 - P(x=0)] 1 - P(x=0) 0.8 [ 1-0.27 1 - 0.2 0.8 X 0.8 0.8 i PCX!!), p(x, 1) = 0.8 ESP