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There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected? Probabilty of choosing 1 girl 10/25 Probability of choosing 1st boy 15/24 Probability of choosing 2nd boy 14/23 No of ways 1 girl and 2 boys can be choosen 3! Totol probability 10/25*15/24*14/23 *3!?
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There are 15 boys and 10 girls in a class. If three students are selec...
Calculation of Probability:

- We are given that there are 15 boys and 10 girls in a class.
- We need to find the probability of selecting 1 girl and 2 boys out of a total of 25 students.
- To do this, we need to calculate the probability of selecting each individual student and then multiply them together.

Probability of Choosing 1 Girl:
- There are 10 girls in the class, so the probability of selecting a girl as the first student is 10/25.
- After selecting the first girl, there are 24 students left, including 14 boys and 10 girls.
- Therefore, the probability of selecting a boy as the second student is 15/24.
- After selecting the first two students, there are 23 students left, including 13 boys and 10 girls.
- Therefore, the probability of selecting a boy as the third student is 14/23.

Number of Ways to Choose 1 Girl and 2 Boys:
- To calculate the number of ways to choose 1 girl and 2 boys, we use the concept of combinations.
- The number of ways to choose 1 girl out of 10 is 10C1 = 10.
- The number of ways to choose 2 boys out of 15 is 15C2 = 105.
- Therefore, the total number of ways to choose 1 girl and 2 boys is 10 * 105 = 1050.

Total Probability:
- Now, we can calculate the total probability by multiplying the probabilities of choosing each individual student and the number of ways to choose 1 girl and 2 boys.
- Total Probability = (10/25) * (15/24) * (14/23) * (3!) = (10/25) * (15/24) * (14/23) * 6 = 0.1304

Conclusion:
- The probability of selecting 1 girl and 2 boys out of a class of 25 students is 0.1304 or 13.04%.
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Answer the following question based on the information given below.In an election for the prefectorial body of a school three students Dev, Praveen and Xamim have been nominated to be elected as the Head boy. Each student can choose to vote either one of them or any two of the three nominated candidates but all students have to vote compulsorily.While counting it has been observed that students from all standards except 8th, 9th and 10th have voted for all the three candidates in equal numbers. The students from standard 8 voted for only Dev and Xamim, students from standard 9 did not vote for Dev. The students of standard 10 voted for all of them, however no student voted for both Dev and Praveen. The total number of votes from 8th standard is equal to 140, the number of students from 9th standard who voted for Xamim is 70. The total number of students in standard 10 is 150 out of which the number of students in standard 10 who caste only one vote is 120. The total number of students who caste exactly two votes is 130. Also, each of the candidates had to campaign in at least two classes(standards) to put forward their ideas. The candidates get votes from a class if and only if he campaign in that class.Q.If a student from 10th standard is known to have voted for Xamim then find the probability that he will vote for Praveen.(Use data from the previous questions, if require d).Note: No vote is trasferred.

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?

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There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected? Probabilty of choosing 1 girl 10/25 Probability of choosing 1st boy 15/24 Probability of choosing 2nd boy 14/23 No of ways 1 girl and 2 boys can be choosen 3! Totol probability 10/25*15/24*14/23 *3!?
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There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected? Probabilty of choosing 1 girl 10/25 Probability of choosing 1st boy 15/24 Probability of choosing 2nd boy 14/23 No of ways 1 girl and 2 boys can be choosen 3! Totol probability 10/25*15/24*14/23 *3!? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected? Probabilty of choosing 1 girl 10/25 Probability of choosing 1st boy 15/24 Probability of choosing 2nd boy 14/23 No of ways 1 girl and 2 boys can be choosen 3! Totol probability 10/25*15/24*14/23 *3!? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected? Probabilty of choosing 1 girl 10/25 Probability of choosing 1st boy 15/24 Probability of choosing 2nd boy 14/23 No of ways 1 girl and 2 boys can be choosen 3! Totol probability 10/25*15/24*14/23 *3!?.
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