Algebra 1, probability

Question

an urn contains 9 gray marbles and 10 purple marbles. ryan chooses one marble randomly and then another marble randomly. what is the probability that he picks two purple marbles, if he replaces the first marble or doesnt replace the first marble

Answer 1

If Ryan replaces the first marble, then the probability of picking a purple marble on the first draw is 10/19. The probability of picking another purple marble on the second draw is also 10/19. Therefore, the probability of picking two purple marbles, WITH, is:

(10/19) * (10/19) = 100/361, or approximately 0.277

If Ryan doesn't replace the first marble, then the probability of picking a purple marble on the first draw is 10/19. However, since the first marble is not replaced, there are only 9 purple marbles and 18 total marbles left in the urn for the second draw.

Therefore, the probability of picking another purple marble on the second draw is 9/18, or 1/2.

Therefore, the probability of picking two purple marbles, WITHOUT replacement, is:

(10/19) * (9/18) = 45/171, or approximately 0.263

So the probability of picking two purple marbles is higher if Ryan replaces the first marble.