JEE MAIN - Mathematics (2018 (Offline) - No. 8)
A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and
this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at
random from the bag, then the probability that this drawn ball is red, is :
$${3 \over 4}$$
$${3 \over 10}$$
$${2 \over 5}$$
$${1 \over 5}$$
Giải thích
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If we follow path 1, then probability of getting 1st ball black $$ = {6 \over {10}}$$ and probability of getting 2nd ball red when there is 4 R and 8 B balls = $${4 \over {12}}$$.
So, the probability of getting 1st ball black and 2nd ball red = $${6 \over {10}} \times {4 \over {12}}$$.
If we follow path 2, then the probability of getting 1st ball red $$ = {4 \over {10}}$$ and probability of getting 2nd ball red when in the bag there is 6 red and 6 black balls = $${6 \over {12}}$$
$$\therefore\,\,\,$$ Probability of getting 2nd ball as red
$$ = {6 \over {10}} \times {4 \over {12}} + {4 \over {10}} \times {6 \over {12}}$$
$$ = {1 \over 5} + {1 \over 5}$$
$$ = {2 \over 5}$$