a bag contains 5 white balls. the following process is repeated. A ball is drawn uniformly at random from the bag(that is each of 5 balls of equal probability=1/5 of being drawn in each trial ).If colour of the drawn ball is white then it is coloured with black and put into the bag. if the colour of the drawn ball is black then it is put into the bag
without changing its colour what is the expected number of times upto two decimal places this process is repeated so that the bag contains only black balls
Answers
(just check wether the answer is correct)
A bag contains 5 white balls. the following process is repeated. A ball is drawn uniformly at random from the bag(that is each of 5 balls of equal probability=1/5 of being drawn in each trial )
Explanation:
First ball:
Probability of drawing a white ball = 5 ÷ 8
Probability of drawing a black ball = 3 ÷ 8
Second ball:
This depends on the first ball drawn, lets say you drew a white ball initially, 4 white balls are left out of 7 balls in total.
The probability of a white ball in the second pick = 4 ÷ 7.
Total probability of drawing two white balls = 5 ÷ 8 × 4 ÷ 7
If you picked a black ball initially, picking another black ball would have a probability of 2 ÷ 7.
Similarly, total probability for 2 blacks = 3 ÷ 8 × 2 ÷ 7 ⇒ 3 ÷ 28
The bag contains only black bags = 0.10
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