A coin is tossed thrice and all eight outcomes are assumed equally likely. Find whether the events E -Maths 9th

A coin is tossed thrice and all eight outcomes are assumed equally likely. Find whether the events E -Maths 9th
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Answer :

When a coin is tossed three times, the sample space is given by S = [HHH, HHT, HTH, THT, THH, HTT, TTH, TTT] E = {HHH, HTT, THT, TTH}, F = {TTT, HTH, THH, HHT}E ∩ F = ϕP(E) = \(rac{4}{8}\) = \(rac{1}{2}\), P(F) = \(rac{4}{8}\) = \(rac{1}{2}\), P(E ∩ F) = ϕP(E) . P(F) = \(rac{1}{2}\) x \(rac{1}{2}\) x \(rac{1}{4}\) ≠ P(E ∩ F) ∴ E and F are not independent events.
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Related questions

Let a pair of fair coins be tossed. Here S = {HH, HT, TH, TT}. Consider the events A = {heads on the first coin} = {HH, HT}, -Maths 9th

Description : Let a pair of fair coins be tossed. Here S = {HH, HT, TH, TT}. Consider the events A = {heads on the first coin} = {HH, HT}, -Maths 9th

Last Answer : ThenP (A) = P (B) = P (C) = \(rac{2}{4}\) = \(rac{1}{2}\) andP (A ∩ B) = P ({HH}) = \(rac{1}{4}\), P (A ∩ C) = P ({HT}) = \(rac{1}{4}\)P ( ... C)Thus condition (i) is satisfied, i.e., the events are pairwise independent. But condition (ii) is not satisfied and so the three events are not independent

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Last Answer : Required probability = P(0 heads) + P(1 head) = 250/1000 + 550 / 1000 = 800/ 1000 =4 / 5 =0.8

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes ; -Maths 9th

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Last Answer : Total number of chances = 23 + 72 + 77 + 28 = 200 Number of chances of coming 2 heads = 72 therefore P( coming 2 heads)= 514 / 642 = 9 / 25

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes -Maths 9th

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Last Answer : It is given that coin is tossed 200 times Total number of trials = 200 Number of events for getting less than three tails = 68 + 82 + 30 = 180 Probability of getting less than 3 tails =180 / 200 =9 / 10

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Last Answer : Required probability = P(0 heads) + P(1 head) = 250/1000 + 550 / 1000 = 800/ 1000 =4 / 5 =0.8

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Last Answer : Total number of chances = 23 + 72 + 77 + 28 = 200 Number of chances of coming 2 heads = 72 therefore P( coming 2 heads)= 514 / 642 = 9 / 25

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Last Answer : It is given that coin is tossed 200 times Total number of trials = 200 Number of events for getting less than three tails = 68 + 82 + 30 = 180 Probability of getting less than 3 tails =180 / 200 =9 / 10

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Last Answer : P (at most one head) = P (0 head) + P (1 head) = 250/1000 + 550/1000 = 800/1000 = 4/5

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Last Answer : Given, Total number of events = 500 No. of times heads occur = 285 Probability of getting head when coin is tossed at random = 285/500 = 57/100 No. of times tails occur = 215 Probability of getting tails when coin is tossed at random = 215/500 = 43/100

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Last Answer : Given, Total number of events = 400 (a) No. of times two heads occur = 112 Probability of getting two heads = 112/400 = 7/25 (b) No. of times one heads occur = 160 Probability of getting one heads = 160/400 = 2/5 (c) No. of times no heads occur = 128 Probability of getting no heads = 128/400 = 8/25

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Last Answer : B 180 300

ECE Board Exam March 1996 According to the Nyquist theorem, the sampling rate that can be used in a PCM system is ________ the highest audio frequency. A. once B. eight times C. twice D. thrice

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Description : A and B throw a coin alternately till one of them gets a ‘head’ and wins the game. Find their respective probabilities of winning . -Maths 9th

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A cylindrical rod of iron whose height is eight times its radius is melted and cast into spherical balls each of half the radius of the cylinder. -Maths 9th

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Description : What do you mean by Mutually Exclusive Events? -Maths 9th

Last Answer : The events are said to be mutually exclusive if they cannot occur simultaneously in a single draw. Events such as tossing a head or a tail with a coin, drawing a queen or a jack from a pack of cards, ... the card can be the king of spades. Similarly for B and C, the card can be king of hearts.

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Last Answer : Let A, B and C be any two events associated with a random experiment whose sample space is S. Then, (i) A ∪ B. (Union of A and B) is the event that occurs if A occurs or B occurs or both A and B occur ... a mutually exclusive and exhaustive set of events. ∴ A∩B = ϕ, B∩C = ϕ, A ∩C = ϕ and A∪B∪C = S.