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📐 Mathematics  ·  Probability  ·  JEE

Box 1 has 2 white and 3 black balls; Box 2 has 4 white and 1 black. A box is chosen at random and a white ball is drawn. The probability it came from Box 1 is:

Answer: 1/3.

  • A 1/3
  • B 2/3
  • C 2/5
  • D 1/2

Correct answer: A. 1/3

Explanation: By Bayes: (1/2·2/5)/(1/2·2/5 + 1/2·4/5) = (2/5)/(6/5) = 1/3.

UABA and BA onlyB onlyOutside both circles: complement of (A union B)

Venn diagram of the universal set U with events A and B, showing the intersection (A and B), the parts unique to each event, and the complement region outside both.

Concept context

Chance, events, conditional probability, and Bayes theorem

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