Question

A bag contains 2 white and 2 black balls. a ball is drawn at random. if it is white, it is not replaced into the urn, otherwise it is replaced along with another ball of the same color. the process is repeated. find the probability that the third ball drawn is black

Answer 1

white 2 ,black 2
total balls =4
first que...
white probability=2/4=1/2

second que...
white not probability=2/4=1/2

Answer 2

Answer:

$Probability\:that\:third\:ball\:drawn\:is\:black=\frac{49}{72}$

Step-by-step explanation:

Total Balls = 4

Probability of getting a black ball = $\frac{2}{4}=\frac{1}{2}$

Probability of getting a White ball = $\frac{2}{4}=\frac{1}{2}$

Following are the only way in which we can get 3rd black ball:

BBB , BWB , WBB & WWB

Probability = Probability (BBB) + Probability (BWB) + Probability (WBB)

                     + Probability (WWB)

$Probablity\,=\,\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{2}\times\frac{2}{3}+\frac{1}{2}\times\frac{2}{3}\times\frac{2}{3}+\frac{1}{2}\times\frac{1}{3}\times$

$Probability=\frac{49}{72}$

Therefore, $Probability\:that\:third\:ball\:drawn\:is\:black=\frac{49}{72}$