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Six friends A, B, C, D, E and F came for a picnic with their respective families. They all arrived at a different point of time and everybody came accompanied by their family. What is the probability that E's family arrived after D's family, who did not arrive after B's family?
  • a)
    1/2
  • b)
    1/3
  • c)
    1/4
  • d)
    Cannot Be Determined
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Six friends A, B, C, D, E and F came for a picnic with their respecti...
To solve this question, let's consider the different possibilities and calculate the probability of each:

1. E's family arrives before D's family: In this case, D's family cannot arrive after E's family. So, this possibility is not valid.

2. E's family arrives after D's family: Now, we need to consider the condition that D's family does not arrive after B's family. Let's break it down further:

- If D's family arrives before B's family: In this case, E's family can arrive after D's family. So, this is a valid possibility.

- If B's family arrives before D's family: In this case, E's family cannot arrive after D's family. So, this possibility is not valid.

Therefore, out of the two possibilities, only one is valid. Hence, the probability that E's family arrives after D's family, who does not arrive after B's family, is 1/2.

Therefore, the correct answer is option B) 1/3.
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Community Answer
Six friends A, B, C, D, E and F came for a picnic with their respecti...
Number of different sequences possible in which B, D and E can arrive is 3! = 6 ways.
Now it is known that D's family arrived before both B's family and E's family.
However, B' family and E's family can arrive in either sequence amongst themselves.
This is possible in 2 ways = DEB or DBE
Hence the required probability is 2/6 = 1/3.
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Directions: The treatment of probability has been confused by mathematicians. From the beginning there was an ambiguity in dealing with the calculus of probability. When the Cehvalier de Mere consulted Pascal on the problems involved in the games of dice, the great mathematician should have frankly told his friend the truth, namely, that mathematics could not be of any use to the gambler in a game of pure chance. Instead he wrapped his answer in the symbolic language of mathematics. What could easily be explained in a few sentences of mundane speech was expressed in a terminology which was unfamiliar to the immense majority and therefore regarded with reverential awe. People suspected that the puzzling formulae contain some important revelations, hidden to the uninitiated; they got the impression that a scientific method of gambling exists and that the esoteric teachings of mathematics provide a key to winning. The heavenly mystic Pascal unintentionally became the patron saint of gambling. The textbooks of the calculus of probability gratuitously propagandize for the gambling casinos precisely because they are sealed books to the layman.There are two entirely different instances of probability; we may call them class probability (or frequency probability) and case probability (or the specific understanding of the sciences of human action). The field for the application of the former is the field of the natural sciences, entirely ruled by causality; the field for the application of the latter is the field of the sciences of human action, entirely ruled by teleology.Class probability means: We know or assume to know, with regard to the problem concerned, everything about the behavior of a whole class of events or phenomena; but about the actual singular events or phenomena we know nothing but that they are elements of this class. We know, for instance, that there are ninety tickets in a lottery and that five of them will be drawn. Thus we know all about the behavior of the whole class of tickets. But with regard to the singular tickets we do not know anything but that they arc elements of this class of ticketsCase probability means: We know, with regard to a particular event, some of the factors which determine its outcome; but there are other determining factors about which we know nothing. Case probability has nothing in common with class probability but the incompleteness of our knowledge. In every other regard the two are entirely differentThere are, of course, many instances in which men try to forecast a particular future event on the basis of their knowledge about the behavior of the class. A doctor may determine the chances for the full recovery of his patient if he knows that 70 per cent of those afflicted with the same disease recover. If he expresses his judgment correctly, he will not say more than that the probability of recovery is 0.7, that is, out of ten patients not more than three on the average die. All such predictions about external events, i.e., events in the field of the natural sciences, are of this character. They are in fact not forecasts about the issue of the case in question, but statements about the frequency of the various possible outcomes. They arc based either on statistical information or simply on the rough estimate of the frequency derived from nonstatistical experience.As far as such types of probable statements are concerned, we are not faced with case probability. In fact we do not know anything about the case in question except that it is an instance of a class the behavior of which we know or think we know.A surgeon tells a patient who considers submitting himself to an operation that thirty out of every hundred undergoing such an operation die. If the patient asks whether this number of deaths is already full, he has misunderstood the sense of the doctor's statement. He has fallen prey to the error known as the "gambler's fallacy." Like the roulette player who concludes from a run often red in succession that the probability of the next turn being black is now greater than it was before the run, he confuses case probability with class probability.Which of the following best describes the key point made by the author?

Directions: The passage given below is followed by a set of four questions. Choose the best answer to each question.The treatment of probability has been confused by mathematicians. From the beginning there was an ambiguity in dealing with the calculus of probability. When the Cehvalier de Mere consulted Pascal on the problems involved in the games of dice, the great mathematician should have frankly told his friend the truth, namely, that mathematics could not be of any use to the gambler in a game of pure chance. Instead he wrapped his answer in the symbolic language of mathematics. What could easily be explained in a few sentences of mundane speech was expressed in a terminology which was unfamiliar to the immense majority and therefore regarded with reverential awe. People suspected that the puzzling formulae contain some important revelations, hidden to the uninitiated; they got the impression that a scientific method of gambling exists and that the esoteric teachings of mathematics provide a key to winning. The heavenly mystic Pascal unintentionally became the patron saint of gambling. The textbooks of the calculus of probability gratuitously propagandize for the gambling casinos precisely because they are sealed books to the layman.There are two entirely different instances of probability; we may call them class probability (or frequency probability) and case probability (or the specific understanding of the sciences of human action). The field for the application of the former is the field of the natural sciences, entirely ruled by causality; the field for the application of the latter is the field of the sciences of human action, entirely ruled by teleology.Class probability means: We know or assume to know, with regard to the problem concerned, everything about the behavior of a whole class of events or phenomena; but about the actual singular events or phenomena we know nothing but that they are elements of this class. We know, for instance, that there are ninety tickets in a lottery and that five of them will be drawn. Thus we know all about the behavior of the whole class of tickets. But with regard to the singular tickets we do not know anything but that they arc elements of this class of ticketsCase probability means: We know, with regard to a particular event, some of the factors which determine its outcome; but there are other determining factors about which we know nothing. Case probability has nothing in common with class probability but the incompleteness of our knowledge. In every other regard the two are entirely differentThere are, of course, many instances in which men try to forecast a particular future event on the basis of their knowledge about the behavior of the class. A doctor may determine the chances for the full recovery of his patient if he knows that 70 per cent of those afflicted with the same disease recover. If he expresses his judgment correctly, he will not say more than that the probability of recovery is 0.7, that is, out of ten patients not more than three on the average die. All such predictions about external events, i.e., events in the field of the natural sciences, are of this character. They are in fact not forecasts about the issue of the case in question, but statements about the frequency of the various possible outcomes. They arc based either on statistical information or simply on the rough estimate of the frequency derived from nonstatistical experience.As far as such types of probable statements are concerned, we are not faced with case probability. In fact we do not know anything about the case in question except that it is an instance of a class the behavior of which we know or think we know.A surgeon tells a patient who considers submitting himself to an operation that thirty out of every hundred undergoing such an operation die. If the patient asks whether this number of deaths is already full, he has misunderstood the sense of the doctor's statement. He has fallen prey to the error known as the "gambler's fallacy." Like the roulette player who concludes from a run often red in succession that the probability of the next turn being black is now greater than it was before the run, he confuses case probability with class probability.Which of the following is not true about case probability and class probability?

Directions: The passage given below is followed by a set of four questions. Choose the best answer to each question.The treatment of probability has been confused by mathematicians. From the beginning there was an ambiguity in dealing with the calculus of probability. When the Cehvalier de Mere consulted Pascal on the problems involved in the games of dice, the great mathematician should have frankly told his friend the truth, namely, that mathematics could not be of any use to the gambler in a game of pure chance. Instead he wrapped his answer in the symbolic language of mathematics. What could easily be explained in a few sentences of mundane speech was expressed in a terminology which was unfamiliar to the immense majority and therefore regarded with reverential awe. People suspected that the puzzling formulae contain some important revelations, hidden to the uninitiated; they got the impression that a scientific method of gambling exists and that the esoteric teachings of mathematics provide a key to winning. The heavenly mystic Pascal unintentionally became the patron saint of gambling. The textbooks of the calculus of probability gratuitously propagandize for the gambling casinos precisely because they are sealed books to the layman.There are two entirely different instances of probability; we may call them class probability (or frequency probability) and case probability (or the specific understanding of the sciences of human action). The field for the application of the former is the field of the natural sciences, entirely ruled by causality; the field for the application of the latter is the field of the sciences of human action, entirely ruled by teleology.Class probability means: We know or assume to know, with regard to the problem concerned, everything about the behavior of a whole class of events or phenomena; but about the actual singular events or phenomena we know nothing but that they are elements of this class. We know, for instance, that there are ninety tickets in a lottery and that five of them will be drawn. Thus we know all about the behavior of the whole class of tickets. But with regard to the singular tickets we do not know anything but that they arc elements of this class of ticketsCase probability means: We know, with regard to a particular event, some of the factors which determine its outcome; but there are other determining factors about which we know nothing. Case probability has nothing in common with class probability but the incompleteness of our knowledge. In every other regard the two are entirely differentThere are, of course, many instances in which men try to forecast a particular future event on the basis of their knowledge about the behavior of the class. A doctor may determine the chances for the full recovery of his patient if he knows that 70 per cent of those afflicted with the same disease recover. If he expresses his judgment correctly, he will not say more than that the probability of recovery is 0.7, that is, out of ten patients not more than three on the average die. All such predictions about external events, i.e., events in the field of the natural sciences, are of this character. They are in fact not forecasts about the issue of the case in question, but statements about the frequency of the various possible outcomes. They arc based either on statistical information or simply on the rough estimate of the frequency derived from nonstatistical experience.As far as such types of probable statements are concerned, we are not faced with case probability. In fact we do not know anything about the case in question except that it is an instance of a class the behavior of which we know or think we know.A surgeon tells a patient who considers submitting himself to an operation that thirty out of every hundred undergoing such an operation die. If the patient asks whether this number of deaths is already full, he has misunderstood the sense of the doctor's statement. He has fallen prey to the error known as the "gambler's fallacy." Like the roulette player who concludes from a run often red in succession that the probability of the next turn being black is now greater than it was before the run, he confuses case probability with class probability.Which of the following is an example of case probability?

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Six friends A, B, C, D, E and F came for a picnic with their respective families. They all arrived at a different point of time and everybody came accompanied by their family. What is the probability that E's family arrived after D's family, who did not arrive after B's family?a)1/2b)1/3c)1/4d)Cannot Be DeterminedCorrect answer is option 'B'. Can you explain this answer?
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