Consider a box that contains 14 red balls,12 blue balls, and 9 yellow balls. a ball is drawn at random and the color is noted and then put back inside the box. then, another ball is drawn at random. find the probability that: a. both are blue b. the first is red and the second is yellow

a.

b.

Step-by-step explanation:

We have been given that a box contains 14 red balls,12 blue balls,and 9 yellow balls.A ball is drawn at random and the color is noted and then put back inside the box.Then, another ball is drawn at random.

a. Since the balls are being replaced after each draw, so the probability of any two events will be independent.  

As ball is replaced so number of total balls and each color ball will be same.  The probability of getting second blue ball will be 12/35. So by the multiplication rule of probability for independent events:

Therefore, probability of getting two blue balls will be 0.117551.

b. Let us find probability of getting a red ball.

By the multiplication rule of probability for independent events probability of getting a red then yellow ball will be:

Therefore, probability of getting first a red and then a yellow ball is 0.1028571.