Question

2. A bag contains 24 red marbles and 6 blue marbles. We select 4 marbles from the bag at random. (b) What is
the probability at least one of the marbles is blue. (b) What is the probability at most one of the selected marbles
is blue.

Answer 1

Total marbles = 24 + 6 = 30

a) P(at least one marble is blue) = 1 - P(none of the marble is blue)

                                                    = 1 - (24C4 / 30C4)

                                                    = 1 - (10626 / 27405)

                                                    = 0.6123

b) P(at most one marble is blue) = P(none of the marble is blue) + P(one of the marble is blue)

                                                    = (24C4 / 30C4) + (24C3 * 6C1 / 30C4)

                                                    = (10626 / 27405) + (2024 * 6 / 27405)

                                                    = 0.8309