Question

A bag has 4 yellow, 6 red, 2 green, and 8 purple marbles. What is the probability of picking a purple marble, not replacing it, and then picking another purple marble?

Answer 1

The probability of picking two consecutive purple marbles without replacement is 14.72%.

Explanation:

Initially, there are 4+6+2+8 = 20 total marbles.

The probability of picking a purble marble is

P_{1} = \frac{number of purple marbles}{number of total marbles}

P_{1}= \frac{8}{20} = 0.4

Since there are no replacements, there are now 19 total marbles, 7 of which are purple. So, the probability of picking another purple marble is

P_{2} = \frac{7}{19} = 0.368

The probability P of picking a purble marble(P_{1}), not replacing it, and then picking another purple marble(P_{2}) is:

P = P_{1}*P_{2} = 0.4*0.368 = 0.1472 = 14.72%