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A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four balls are picked at random,
Quantity I: Probability that at least one is Black.
Quantity II: Probability that all is Black.
  • a)
    Quantity I > Quantity II
  • b)
    Quantity I < Quantity II
  • c)
    Quantity I ≥ Quantity II
  • d)
    Quantity I ≤ Quantity II
  • e)
    Quantity I = Quantity II or relation cannot be established
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four ba...
Total Balls = 15
Probability = 11c4/15c4 = 22/91
One is black = 1 – 22/91 = 69/91
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Most Upvoted Answer
A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four ba...
To calculate the probability, we need to find the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes when picking 4 balls from a basket of 15: C(15,4) = 1365

Quantity I: Probability that at least one ball is Black.
The number of favorable outcomes is the sum of the following possibilities:
1. One black ball and three non-black balls: C(4,1) * C(11,3) = 440
2. Two black balls and two non-black balls: C(4,2) * C(11,2) = 330
3. Three black balls and one non-black ball: C(4,3) * C(11,1) = 44
4. Four black balls: C(4,4) = 1

Total number of favorable outcomes for Quantity I: 440 + 330 + 44 + 1 = 815

Quantity I: Probability that at least one ball is Black = favorable outcomes / total outcomes = 815 / 1365 ≈ 0.598

So, Quantity I is approximately 0.598.

Quantity II: Probability that all balls are Black.
The number of favorable outcomes is the number of ways to choose 4 black balls: C(4,4) = 1

Quantity II: Probability that all balls are Black = favorable outcomes / total outcomes = 1 / 1365 ≈ 0.001

So, Quantity II is approximately 0.001.

Therefore, the answer is:
a) Quantity I > Quantity II
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A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four balls are picked at random,Quantity I: Probability that at least one is Black.Quantity II: Probability that all is Black.a)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'A'. Can you explain this answer?
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