Question

You have seven green marbles, three red marbles, and two blue marbles in a bag. Suppose you pick three marbles at random from the bag and do not replace them. What is the probability that all three marbles are green? (Write you answer as a decimal and round your answer to 2 places after the decimal point. For example, an answer of 0.7829 should be rounded to 0.78.)

Answer 1

seven green marbles, three red marbles, and two blue marbles

Total marbles = 7 + 3 + 2 = 12

P[ Selecting all three green marbles from 12 ] = Selecting 3 marble out of 7 / selecting 3 marble out of 12

P[ Selecting all three green marbles from 12 ] = 7C3 / 12C3

P[ Selecting all three green marbles from 12 ] = (7*6*5/3*2*1)/(12*11*10/3*2*1)

P[ Selecting all three green marbles from 12 ] = 35/220

P[ Selecting all three green marbles from 12 ] = 0.1591

P[ Selecting all three green marbles from 12 ] = 0.16