\Find \P(\A), \If \P(\B) = 2/3, \P(\A \cup \B) = 4/7, \P(\A \cap \B) = 1/3

Haryana Police Constable Model Paper 5

Question : 85 of 100

Marks: +1, -0

\Find \P(\A), \If \P(\B) = 2/3, \P(\A ∪ \B) = 4/7, \P(\A ∩ \B) = 1/3

Solution:

Given:

\P(\B) = 2/3

\P(\A ∪ \B) = 4/7

\P(\A ∩ \B) = 1/3

Formula used:

\P(\A ∪ \B) = \P(\A) + \P(\B)-\P(\A∩ \B)

Calculation:

\P(\A ∪ \B) = \P(\A) + \P(\B)-\P(\A∩ \B)

⇒ 4/7 = \P(\A) + 2/3-1/3

⇒ \P(\A) = 4/7 + 1/3-2/3

⇒ (12 +7-14)/21

⇒ 5/21

$∴ \The \value \of \P(\A) \is 5/21$

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