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Solve the following question and mark the best possible option.
Two numbers are selected at random without replacement from amongst the first six natural numbers. What is the probability that the minimum of the two is less than 4?
  • a)
    1/15
  • b)
    14/15
  • c)
    2/5
  • d)
    4/5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Solve the following question and mark the best possible option.Two num...
The total number of ways of selecting the two numbers is 6 × 5 = 30.
We want that the minimum of the two numbers is less than 4.
If the smaller number is 1, then the other number can be any of the remaining 5 numbers from 2 to 6.
If the smaller number is 2, then the other number can be any of the remaining 4 numbers from 3 to 6.
If the smaller number is 3, then the other number can be any of the remaining 3 numbers from 4 to 6.
These are 12 cases.
Since the numbers can be interchanged, the toal number of favourable outcomes is 2 × 12 = 24.
Thus the required probability is 24/30 = 4/5
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Most Upvoted Answer
Solve the following question and mark the best possible option.Two num...
To solve this problem, we can start by listing all the possible outcomes of selecting two numbers without replacement from the first six natural numbers:

{1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6},
{2, 3}, {2, 4}, {2, 5}, {2, 6},
{3, 4}, {3, 5}, {3, 6},
{4, 5}, {4, 6},
{5, 6}

There are a total of 15 possible outcomes.

Next, we need to find the favorable outcomes, i.e., the outcomes where the minimum of the two selected numbers is less than 4. We can see that the favorable outcomes are:

{1, 2}, {1, 3}, {2, 3}

There are a total of 3 favorable outcomes.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Favorable outcomes / Total outcomes
= 3 / 15
= 1 / 5
= 0.2

Since the probability is a fraction, we can simplify it further:

Probability = 1 / 5
= (1/5) * (1/1)
= 1/5
= 1:5

Therefore, the probability that the minimum of the two selected numbers is less than 4 is 1:5, which is equivalent to 1/5 or 0.2.

Hence, the correct answer is option D) 4/5.
Free Test
Community Answer
Solve the following question and mark the best possible option.Two num...
The total number of ways of selecting the two numbers is 6 × 5 = 30.
We want that the minimum of the two numbers is less than 4.
If the smaller number is 1, then the other number can be any of the remaining 5 numbers from 2 to 6.
If the smaller number is 2, then the other number can be any of the remaining 4 numbers from 3 to 6.
If the smaller number is 3, then the other number can be any of the remaining 3 numbers from 4 to 6.
These are 12 cases.
Since the numbers can be interchanged, the toal number of favourable outcomes is 2 × 12 = 24.
Thus the required probability is 24/30 = 4/5
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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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Solve the following question and mark the best possible option.Two numbers are selected at random without replacement from amongst the first six natural numbers. What is the probability that the minimum of the two is less than 4?a)1/15b)14/15c)2/5d)4/5Correct answer is option 'D'. Can you explain this answer?
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