NCERT Class XI Mathematics - Probability - Solutions
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Question : 39
Total: 54
Events E and F are such that P(not E or not F) = 0.25. State whether E and F are mutually exclusive.
Solution:
not E or not F = E′ ∪ F′ = (E ∩ F)′ (De Morgan’s Law)
∴ P(not E or not F) = P(E ∩ F)′ = 1 – P (E ∩ F) ⇒ 0.25 = 1 – P(E ∩ F)
⇒ P(E ∩ F) = 1 – 0.25 = 0.75 ≠ 0
∴ Events E and F are not mutually exclusive
∴ P(not E or not F) = P(E ∩ F)′ = 1 – P (E ∩ F) ⇒ 0.25 = 1 – P(E ∩ F)
⇒ P(E ∩ F) = 1 – 0.25 = 0.75 ≠ 0
∴ Events E and F are not mutually exclusive
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