A bag contains 5 white and 3 black balls. Four balls are successively drawn out without replacement. What is the probability that they are alternately of different colours?
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A bag contrains 4 white and 5 black blls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and t
Here, `W_(1)` = {4 white balls} and `B_(1)`={5 black balls} and `W_(2)` = {9white balls} and `B_(2)` = {7 black balls} Let E, is the event that ball transferred fram...
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A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. One bag is chosen at random. From teh selected bag, one b
Bag I ={3B,2W],Bag II={2B,4W} Let `E_(1)`=Event that bag I is selected `E_(2)`=Event that bag II is selected and E=Event that a black ball is selected `rArrP(E_(1))=1//2,P(E_(2))=1/2,P(E//E_(1))=3/5,P(E//E_(2))=2/6=1/3` `thereforeP(E)=P(E_(1))cdotP(E//E_(1))+P(E_(2))cdotP(E//E_(2))` `1/2cdot3/5+1/2cdot2/6=3/10+2/12` `=(18+10)/60=28/60=7/15`
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Three bags contain a number of red and white balls as follows Bag I : 3 red balls, Bag II : 2 red balls and 1 white balls and Bag III : 3 white balls.
Bag I : 3 red balls and 0 white ball Bag II : 2 red balls and 1 white ball. Bag III : 0 red ball andf 3 white balls....
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There are three urns containing 2 white and 3 black balls, 3 white and 2 black balls and 4 white and 1 black balls, respectively. There is an equal pr
Let `U_(1)`={2 white, 3 black balls} `U_(2)`={3 white , 2 black balls} and `U_(3)`={4 white ,1 black balls} `thereforeP(U_(1))=P(U_(2))=P(U_(3))=1/3` Let `E_(1)` be the event that a ball is chosen from...
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A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of dr
Probability of drawing 2 green balls and one blue ball `=P_(G)cdotP_(G)cdotP_(B)+P_(B)cdotP_(G)cdotP_(G)+P_(G)cdotP_(B)cdotP_(G)` `=3/8cdot2/7cdot2/6+2/8cdot3/7cdot2/6+3/8cdot2/7cdot2/6` `=1/28+1/28+1/28=3/28`
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Balls are drawn one-by-one without replacement from a box containing 2 black, 4 white and 3 red balls till all the balls are drawn. Find the probabili
To draw 2 black, 4 white, and 3 red balls in order is same as arranging two black balls at first 2 places, 4 white balls at next 4 places,...
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A bag contains 3 red, 7 white, and 4 black balls. If three balls are drawn from the bag, then find the probability that all of them are of the same co
Correct Answer - `(10)/(91)` The required probability is `(.^(3)C_(3) + .^(7)C_(3) + .^(4)C_(3))/(.^(14)C_(3)) = (1 + 35 + 4)/(14 xx 13 xx 2) = (40)/(14 xx 26) = (10)/(91)`
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An urn contains 10 black and 5 white balls. Two balls are drawn from the run one after the other without replacement. What is the probability that fir
Let A nad B denote, respectively, the events that first ball drawn is black and second ball drawn in white. We have to find `P(AnnB) or P(AB).` ` P(AnnB)P(A)P(B//A)` Now,...
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A bag contains `W` white and 3 black balls. Balls are drawn one by one without replacement till all the black balls are drawn. Then find the probabili
Procedure of drawing th balls has to end at the rth draw. So, exactly two black balls are drawn in first (r-1) draws and third black ball is drawn in...
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A bag contains `n` white and `n` red balls. Pairs of balls are drawn without replacement until the bag is empty. Show that the probability that each p
Correct Answer - B The required probability is `(n^(2))/(""^(2n)C_(2))((n-1)^(2))/(""^(2n-2)C_(2))((n-2)^(2))/(""^(2n-4)C_(2))...(2^(2))/(""^(4)C_(2))(1^(2))/(""^(2)C_(2))` `=((1xx2xx3xx4xx...xx(n-1)n)^(2))/(((2n)!)/2^(n))=(2^(n)(n!)^(2))/((2n)!)=(2^(n))/(""^(2n)C_(n))`
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