an urn contains 2 white and 2 black balls. a ball is taken at random. if the ball is white then it is not replaced otherwise it is replaced along with another ball of the same colour. find the probability that the third ball drawn is black.
and your answer is? / let me know what you think first.
list the possibilities:
P(WWW) = 2/4 * 1/3 * 0/2
P(BWW) = 2/4 * 2/5 * 1/4
...
P(BBB) = 2/4 * 3/5 * 4/6
then add up all the ones where the 3rd ball is black.
To find the probability that the third ball drawn is black, we can break down the problem into several steps:
Step 1: Determine the probability of drawing a white ball on the first draw.
Since there are a total of 4 balls in the urn and 2 of them are white, the probability of drawing a white ball on the first draw is 2/4 or 1/2.
Step 2: Determine the probability of drawing a black ball on the first draw.
Similarly, the probability of drawing a black ball on the first draw is also 2/4 or 1/2.
Step 3: Determine the probability of drawing a black ball on the second draw.
If the first ball drawn is black, it gets replaced with another black ball. So, in this case, there will still be 2 black balls out of a total of 4 balls. Therefore, the probability of drawing a black ball on the second draw is also 2/4 or 1/2.
Step 4: Determine the probability of drawing a black ball on the third draw.
Since the first two draws were black, there will be a total of 3 balls left in the urn, out of which 2 are black. Therefore, the probability of drawing a black ball on the third draw is 2/3.
Step 5: Multiply the probabilities from all the steps.
To find the probability of all these independent events happening, we need to multiply the probabilities from each step. Thus, the probability that the third ball drawn is black is (1/2) * (1/2) * (2/3) = 1/6.
Therefore, the probability that the third ball drawn is black is 1/6.