# Example 11 - Chapter 13 Class 12 Probability

Last updated at Feb. 15, 2020 by Teachoo

Last updated at Feb. 15, 2020 by Teachoo

Transcript

Example 11 An unbiased die is thrown twice. Let the event A be ‘odd number on the first throw’ and B the event ‘odd number on the second throw’. Check the independence of the events A and B. Two events A & B are independent if P(A ∩ B) = P(A) . P(B) An unbiased die is thrown twice S = Let us define two events as A : Odd number on the First throw B : Odd number on the Second throw vA : Odd number on First throw A : { (1, 1), (1, 2), ………., (1, 6) (3, 1), (3, 2), ………., (3, 6) (5, 1), (5, 2), ………., (5, 6) } P(A) = 𝟏𝟖/𝟑𝟔 = 𝟏/𝟐 B : Odd number on Second throw B : { (1, 1), (2, 1), ………., (6, 1) (1, 3), (2, 3), ………., (6, 3) (1, 5), (2, 5), ………., (6, 5) } P(A) = 𝟏𝟖/𝟑𝟔 = 𝟏/𝟐 B : Odd number on Second throw B : { (1, 1), (2, 1), ………., (6, 1) (1, 3), (2, 3), ………., (6, 3) (1, 5), (2, 5), ………., (6, 5) } P(A) = 𝟏𝟖/𝟑𝟔 = 𝟏/𝟐 B : Odd number on Second throw B : { (1, 1), (2, 1), ………., (6, 1) (1, 3), (2, 3), ………., (6, 3) (1, 5), (2, 5), ………., (6, 5) } P(A) = 𝟏𝟖/𝟑𝟔 = 𝟏/𝟐 A ∩ B = Odd number on the First & Second throw = { (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)} So, P(A ∩ B) = 9/36 = 1/4 Now, P(A) . P(B) = 1/2 × 1/2 = 1/4 Since P(A ∩ B) = P(A) . P(B), Therefoare, A and B are independent events

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Example 11 Important You are here

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Example 27 Deleted for CBSE Board 2021 Exams only

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Example 34 Important Deleted for CBSE Board 2021 Exams only

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Chapter 13 Class 12 Probability

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.