Question

A bag contains marbles: 5 red, 2 blue, and 1 green. You pick a marble and then another one without replacement. What is the probability you will draw a red and then a green?

Answer 1

hi

1st draw: green

2/12. (2 green out of 12 marbles), reduces to 1/6

2nd draw: blue

4/11 (4 blue marbles out of the 11 marbles remaining after 1st draw.)

Probability of theses BOTH happening: multiply these individual probabilities.

Conditional probability:

P(a and b) = P(a)P(b|a)

Prob(event 1) × Prob(event 2 given event 1).

1/6 • 4/11 = 4/66 = 2/33 or 0.0606. just a hair over 6% probability of the described sequence hapening.