Example 5 A bag contains three purple, six green, five blue, four yellow and two

Question

Example 5 A bag contains three purple, six green, five blue, four yellow and two red marbles. i. What is the probability that two blue marbles are drawn in succession when chosen without replacement? a. ii. Are the events INDEPENDENT or DEPENDENT? b. i. What is the probability that two green marbles are drawn in succession when chosen with replacement? 11. Are the events INDEPENDENT or DEPENDENT? c. What is the conditional probability that, without replacement, the second marble is yellow given the first marble was green?

Explanation / Answer

Total number of marbles = 3+6+5+4+2

= 20

a) i. P(2 blue marbles without replacement) = 5/20 x 4/19

= 0.0526

ii. The events are not independent

b) i. P(two green, with replacement) = 6/20 x 6/20

= 0.09

ii. The events are independent

c) P(second marble is yellow | first marble ws green) = 4/19

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