Question

An urn contains 4 red, 6 yellow, and 3 blue balls. Two balls are drawn at random, one at a time and without replacement. Find the probability that...

a) The first draw is a red ball.
b) The first draw is red or yellow.
c) The second draw is red, given that the first draw is red.
d) The second draw is yellow, given that the first draw is blue.

Answer 1

The probability that the first draw is red is 4/13. The probability that the first draw is red or yellow is 10/13. Given that the first draw is red, the probability of the second draw being red is 1/4. Given that the first draw is blue, the probability of the second draw being yellow is 1/2.

Step-by-step explanation:

To find the probability of each event, we need to determine the number of favorable outcomes and the total number of possible outcomes.

a) The probability that the first draw is a red ball is 4/13. There are 4 red balls out of a total of 13 balls in the urn.

b) The probability that the first draw is red or yellow is [4 red balls + 6 yellow balls] / 13 = 10/13. There are 10 favorable outcomes out of 13 possible outcomes.

c) Given that the first draw is a red ball, there are 3 red balls left in the urn out of a total of 12 balls. So, the probability of the second draw being red is 3/12 = 1/4.

d) Given that the first draw is a blue ball, there are 6 yellow balls left in the urn out of a total of 12 balls. So, the probability of the second draw being yellow is 6/12 = 1/2.