CBSE Class 12-science Answered
The probability of selecting any urn (P) = 1/2.
Let A be the event of chosing urn A
Let B be the event of chosing urn B
The probability of drawing a red marble from urn A (R/A) = 3/5.
The probability of drawing a white marble from urn A (W/A) = 2/5
The probability of drawing a red marble from urn B (R/B) = 2/7
The probability of drawing a white marble from urn B (W/B) = 5/7
a. both marbles are red = (probability of selecting urn A *(probability selecting red marble from urn A)*(probability of selecting red marble from urn B after the marble selected from urn A is also put in the urn B) +(probability of selecting urn B *(probability selecting red marble from urn B)*(probability of selecting red marble from urn A after the marble selected from urn A is also put in the urn A)
Probability = (1/2*3/5*3/8 + 1/2*2/7*4/6)
= 0.1125+0.095
= 0.21
b. both marbles are white = Applying the same logic, we have
Probability = (1/2*2/5*6/8)+(1/2*5/7*3/6) = 0.33
c. both marbles are drawn of same color, so either both marbles are red or both marbles are white. Hence, probability = 0.21+0.33 = 0.54
d. second marble drawn is red, so the first marble drawn from either of the 2 urns can be either red or white. Hence, probability = (1/2*3/5*3/8 + 1/2*2/7*4/6)+(1/2*2/5*2/8)+(1/2*5/7*3/6) = 0.21+0.228 = 0.44
e. marble drawn are of different color So, if first marble drawn is white, then the second is red and so on.
Probability = (1/2*2/5*2/8)+(1/2*5/7*3/6) + (1/2*3/5*5/8)+(1/2*2/7*2/6) = 0.228 +0.235 = 0.46
f. second marble drawn is white So, the first one drawn can be either red or white. Hence,