in Education by
An urn contains 2 white and 2 black balls .A ball is drawn at random.If it is white ,it is not replace into urn ,otherwise it is replaced along with another ball of the same colour .the process is repeated , then find the probabiltiy that the third ball drawn is black. Select the correct answer from above options

1 Answer

0 votes
by
 
Best answer
Correct Answer - B::C Let `B_(i)=` ith ball drawn is black. `W_(i)=` ith ball drawn is white, where I = 1,2 and A= third ball drawn is black. We observe that the black ball can be drawn in the third drawn in one of the following mutually exclusive ways. (i) both first and second balls drawn are white and third ball drawn is black. i.e. `(W_(1)nnW_(2))nnA` (ii) Both first and second balls are black and third ball drawn is black. i.e. `(B_(1)nnB _(2))nnA` (iii) The first ball drawn is white, the second ball drawn is black and the third ball drawn is black. i.e. `(W_(1)nnB_(2))nnA` (iv) The first ball drawn is black, the second ball drawn is white and the third ball drawn is back. i.e. `(B_(1)nnW_(2))nnA` `therefore P(A)=P[{(W_(1)nnW_(2))nnA}uu(B_(1)nnB_(2))nnA}` `uu{(W_(1)nnB_(2))nnA}uu{(B_(1)nnW_(2))nnA}]` `=P{(W_(1)nnW_(2))nnA}+P{(B_(1)nnB_(2))nnA}` `+P(W_(1)NNB_(2))nnA}+P{(B_(1)nnW_(2))nnA} ` `=P(W_(1)nnW_(2))*P(A//(W_(1)nnW_(2)))+P(B_(1)nnB_(2))` `therefore P(A//(B_(1)nnB_(2)))+P(W_(1)nnB_(2))*PP(A//(W_(1)nnB_(2)))` `+P(B_(1)nnW_(2))*P(A//(B_(1)nnW_(2)))` `=((2)/(4)xx(1)/(3))xx1+((2)/(4)xx(3)/(5))xx(4)/(5)` `+((2)/(4)xx(2)/(3))xx(3)/(4)+((2)/(4)xx(2)/(5))xx(3)/(4)` `=(1)/(6)+(1)/(5)+(1)/(4)+(3)/(20)=(23)/(30)`

Related questions

0 votes
    A box contains 2 black, 4 white, and 3 red balls. One ball is drawn at random from the box and kept aside. ... 126` d. none of these Select the correct answer from above options...
asked Nov 13, 2021 in Education by JackTerrance
0 votes
    Threre are 9 red,7 white and 4 black balls in an urn. Two balls are drawn at random from the urn. What will be the ... C. 9 10 D. 8 95 Select the correct answer from above options...
asked Nov 13, 2021 in Education by JackTerrance
0 votes
    A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that: ... of the same colour. Select the correct answer from above options...
asked Nov 13, 2021 in Education by JackTerrance
...