In a large hat you have three blue four red and five purple

In a large hat you have three blue, four red, and five purple marbles. You pick three marvles from this hat, without replacement. Pls show all work.

a) What is the probability of getting two reds and one blue, in that order?

b) What is the probability of getting two reds and one blue in any order?

c) What is the probability of getting three reds, given that the first marble is red?

d) What is the probability of getting three primary colors (blue or red) given that the first marble is blue?

e) What is the probability of getting at least one red marble?

Solution

a) probability of getting two reds and one blue, in that order = (4/12) * (3/11) * (3/10)

                                                                                                = 0.0273

b) probability of getting two reds and one blue in any order = 4C2 * 3C1 / 12C3

                                                                                              = 0.0818

c) probability of getting three reds, given that the first marble is red = prob of getting three reds / prob of getting first marble red

                                                                          = ( 4C3 / 12C3 ) / (4/12)

                                                                          = 3/55 = 0.0545

d) probability of getting three primary colors (blue or red) given that the first marble is blue = prob of getting 3 primary colours out of which first one is blue / Prob of getting first red marble

                                                           = ( 3/12 * 6C2 / 11C2 ) / ( 4/12 )

                                                           = 9/44 = 0.2045

e) probability of getting at least one red marble = 1 - probability of getting no red marble

                                                                           = 1 - 8C3 / 12C3

                                                                           = 41/55 = 0.7455