Question 28 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Given that E and F are events such that P(E) = 0.8, P(F) = 0.7, P (E∩F) = 0.6. Find P (Ē | F̄)

Given that E and F are events such that P(E) = 0.8, P(F) = 0.7, P(E∩F)

Question 28 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

Transcript

Question 28 (Choice 2) Given that E and F are events such that P(E) = 0.8, P(F) = 0.7, P (E ∩ F) = 0.6. Find P(𝐸 ̅|¯𝐹) Now, 𝐏(𝑬 ̅│¯𝑭)=(𝑃(𝐸 ̅ ∩ 𝐹 ̅))/(𝑃(𝐹 ̅)) =(𝑃(𝐸 ∪ 𝐹)^𝐶 )/(1 − 𝑃(𝐹)) =(𝟏 − 𝑷(𝑬 ∪ 𝑭))/(𝟏 − 𝑷(𝑭)) Finding 𝑷(𝑬 ∪ 𝑭) P(E ∪ F) = P(E) + P(F) − P(E ∩ F) Putting values P(E ∪ F) = 0.8 + 0.7 − 0.6 P(E ∪ F) = 0.8 + 0.7 − 0.6 P(E ∪ F) = 0.9 Now, 𝑃(𝐸 ̅│¯𝐹) =(1 − 𝑃(𝐸 ∪ 𝐹))/(1 − 𝑃(𝐹)) =(1 − 0.9)/(1 − 0.7) =0.1/0.3 =𝟏/𝟑

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