A flower shop has 5 yellow roses, 3 red roses and 2 white roses. Martin chooses 3 roses at random. Draw up the probability distribution table for the number of white roses Martin chooses. Can someone please solve this question?

1 Answer
Jan 31, 2018

#"See explanation"#

Explanation:

#"There are 10 roses and 2 of them are white."#
#"So Martin can choose only 0, 1, or 2 white roses."#
#"The odds for him to pick no white rose are : "#
#(8/10)(7/9)(6/8) = (6/10)(7/9) = (2/10)(7/3) = 14/30#
#"The odds to pick 1 white rose are : "#
#C(3,1) (2/10)(8/9)(7/8) = (6/10)(7/9) = 14/30 " also"#
#"The odds for him to pick 2 white roses are :"#
#C(3,2) (2/10)(1/9)(8/8) = (6/10)(1/9) = 2/30#
#"So the pdf is"#
#P("0 white roses") = 14/30#
#P("1 white rose") = 14/30#
#P("2 white roses") = 2/30#
#P("> 2 white roses") = 0#
#"We see that the sum of the probabilities is 1 as should."#

#"Further explanation : "#
#"C(3,1) and C(3,2) because there are 3 possibilities to"#
#"the place of the white rose(s) : first chosen, second, or third ?"#
#"(8/10)(7/9)(6/8) because first there are 10 roses and 8 are not"#
#"white, then 9 roses left and 7 not white, and last 6 on 8."#
#"And so on ... reasoning step by step and flower by flower."#