Question

A bag contains 32 marbles: 4 are red, 9 are black, 12 are blue, 6 are yellow, and 1 is purple. Marbles are drawn one at a time with replacement. What is the probability that (a) The second marble is yellow given the first one was yellow? (b) The second marble is yellow given the first one was black? (c) The third marble is purple given both the first and second were purple?​

Answer 1

Answer: The answer is 6/32 or 0.1875.

Step-by-step explanation:

The question states that the marbles are drawn "with replacement". This means that after a marble is drawn, it is put back into the bag before the next marble is drawn. Therefore, the probability of drawing a yellow marble remains the same for every draw, regardless of what color was drawn previously.

There are 6 yellow marbles out of a total of 32 marbles. So, the probability of drawing a yellow marble is 6/32, which simplifies to 0.1875 when expressed as a decimal.

So, the probability that the second marble is yellow given the first one was yellow is also 0.1875.