One bag contains 3 black and 4 white balls and the other bag contains 4 black and 3 white balls. A die is rolled. -Maths 9th

One bag contains 3 black and 4 white balls and the other bag contains 4 black and 3 white balls. A die is rolled. -Maths 9th
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1 Answer

Answer :

Let A : Getting 2 or 5 B : Getting white ball from first bag C : Getting white ball from second bag.∴ P(A) = \(rac{2}{6}\) = \(rac{1}{3}\) ⇒ P(\(\bar{A}\)) = 1 - P(A) = 1 - \(rac{1}{3}\) = \(rac{2}{3}\)∴ Required probability = First bag white ball + Second bag white ball = P(A) P(B) + P(\(\bar{A}\)) P(C) = \(rac{1}{3}\) x \(rac{4}{7}\) + \(rac{2}{3}\) x \(rac{3}{7}\) = \(rac{4+6}{21}\) = \(rac{10}{21}.\)
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Related questions

A bag contains 5 white, 7 red and 4 black balls. If four balls are drawn one by one with replacement, what is the probability that none is white. -Maths 9th

Description : A bag contains 5 white, 7 red and 4 black balls. If four balls are drawn one by one with replacement, what is the probability that none is white. -Maths 9th

Last Answer : Let A, B, C, D denote the events of not getting a white ball in first, second, third and fourth draw respectively. Since the balls are drawn with replacement, therefore, A, B, C, D are independent events such that P (A) = P (B) ... x \(rac{11}{16}\) x \(rac{11}{16}\) = \(\big(rac{11}{16}\big)^4.\)

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Last Answer : Let A : Event of getting at least 3 black balls Then n(A) = 5C3 x 11C1 + 5C4 (∵ Besides 5 black balls, there are 11 other balls)(3 black + others) (4 black)= \(rac{5 imes4}{2}\) x 11 + 5 = 115Total numbers of ways ... = 1820∴ P(A) = \(rac{n(A)}{n(S)}\) = \(rac{115}{1820}\) = \(rac{23}{364}.\)

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Last Answer : Given, 3 white (3 W), 3 red (3 R), 4 green (4 G), 4 black (4 B) balls Total no. of balls = 3 + 3 + 4 + 4 = 14 Two balls are to be drawn, one by one without replacement. There are 4 possibilities.First BallSecond ... }{13}\) = \(rac{33+33+40+40}{14 imes13}\) = \(rac{146}{182}\) = \(rac{73}{91}.\)

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Last Answer : (d) \(rac{31}{66}\)Total number of balls in the bag = 12 (5 Green + 7 Red) Let S be the sample space of drawing 2 balls out of 12 balls.Thenn(S) = 12C2 = \(rac{12 imes11}{2}\) = 66∴ Let A : Event of drawing two red balls⇒ ... \(rac{n(B)}{n(S)}\) = \(rac{21}{66}\) + \(rac{10}{66}\) = \(rac{31}{66}\).

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A die was rolled 100 times and the number of times, 6 came up was noted. -Maths 9th

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Last Answer : This answer was deleted by our moderators...

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An urn contains nine balls, of which three are red, four are blue and two are green. -Maths 9th

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Description : A cylindrical rod of iron whose radius is one-fourth of its height is melted and cast into spherical balls of the same radius as that of the cylinder. -Maths 9th

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Description : Counters marked 1, 2, 3 are placed in a bag and one is drawn and replaced. -Maths 9th

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A box contains 4 green, 5 red and 6 white balls. Three balls are drawn randomly. What is the probability that the balls drawn are of different colours? a) 24/91 b) 67/91 c) 21/91 d) 70/91 e) 3/13

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Description : A Receptacle contains 3violet, 4purple and 5 black balls. Three balls are drawn at random from the receptacle. The probability that all of them are purple, is: A)3/55 B)7/55 C)1/55 D)9/55

Last Answer : Answer: C) Let S be the sample space. Then, n(S) = number of ways of drawing 3 balls out of 12 = 12C3 = 220 Let E = event of getting all the 3 purple balls. n(E) = 4C3= 4 P(E) = n(E)/n(S) = 4/220 = 1/55

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Description : Two dice are thrown. Find the probability of getting an odd number on the first die and a multiple of 3 on the other. -Maths 9th

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How many possible outcomes when a standard six sided die is rolled?

Description : How many possible outcomes when a standard six sided die is rolled?

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Description : When two dice are rolled, find the probability of getting a greater number on the first die than the one on the second, given that the sum should equal 8. a) 5/18 b) 1/18 c) 2/5 d) 1/5

Last Answer : c) 2/5

What is the probability of the occurrence of a number that is even or less than 3 when a fair die is rolled. a) 2/3 b)3/2 c)5/6 d)6/5

Description : What is the probability of the occurrence of a number that is even or less than 3 when a fair die is rolled. a) 2/3 b)3/2 c)5/6 d)6/5

Last Answer : Answer: A) Let the event of the occurrence of a number that is even be A' and the event of the occurrence of a number that is less than 3 be B'. We need to find P(A or B). P(A) = 3/6 (even numbers = 2,4,6) P(B) = 2/6 ( ... = P(A) + P(B) - P(A or B)  = 3/6 + 2/6 - 1/6 P(A or B) = 4/6=2/3

When a single die is rolled, the sample space is {1,2,3,4,5,6}.What is the probability of getting a 3 when a die is rolled? A) 1/2 B) 1/6 C) 6/1 D) 3/6

Description : When a single die is rolled, the sample space is {1,2,3,4,5,6}.What is the probability of getting a 3 when a die is rolled? A) 1/2 B) 1/6 C) 6/1 D) 3/6

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There are 10 orange, 2 violet and 4 purple balls in a bag. All the 16 balls are drawn one by one and arranged in a row. Find out the number of different arrangements possible. A) 25230 B) 23420 C) 120120 D) 27720

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