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Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the two numbers is less than 4 is (2003S)
  • a)
    1/15
  • b)
    14/15
  • c)
    1/5
  • d)
    4/5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} ...
The minimum of two numbers will be less than 4 if at least one of the numbers is less than 4.
∴ P (at least one no. is < 4), = 1– P (both the no’s are ≥ 4)
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Most Upvoted Answer
Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} ...
Solution:

Probability of selecting two numbers from the set S without replacement = n(S)/(n(S)C2) = 1/15

Let A be the event that minimum of two numbers selected is less than 4.

A = {(1,2), (1,3), (1,4), (2,3), (2,4), (3,4)}

Number of ways of selecting two numbers such that minimum of two numbers is less than 4 = n(A) = 6

Probability of selecting two numbers such that minimum of two numbers is less than 4 = n(A)/n(S)C2 = 6/15 = 2/5

Let B be the event that minimum of two numbers selected is greater than or equal to 4.

B = {(4,5), (4,6), (5,6)}

Number of ways of selecting two numbers such that minimum of two numbers is greater than or equal to 4 = n(B) = 3

Probability of selecting two numbers such that minimum of two numbers is greater than or equal to 4 = n(B)/n(S)C2 = 3/15 = 1/5

Probability of selecting two numbers such that minimum of two numbers is less than 4 or minimum of two numbers is greater than or equal to 4 = P(A) + P(B) = 2/5 + 1/5 = 3/5

Probability of selecting two numbers such that minimum of two numbers is less than 4 = 1 - Probability of selecting two numbers such that minimum of two numbers is greater than or equal to 4 = 1 - 1/5 = 4/5

Hence, the correct answer is option 'D'.
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Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the two numbers is less than 4 is (2003S)a)1/15b)14/15c)1/5d)4/5Correct answer is option 'D'. Can you explain this answer?
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