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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?
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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.
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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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