

Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at Feb. 15, 2020 by Teachoo
Transcript
Example 12 Three coins are tossed simultaneously. Consider the event E ‘three heads or three tails’, F ‘at least two heads’ and G ‘at most two heads’. of the pairs (E,F), (E,G) & (F,G), which are independent? which are dependent? Two events A and B are independent if P(A ∩ B) = P(A) . P(B) Three coins are tossed simultaneously S = {(H, H, H), (H, H, T), (T, H, H), (H, T, H), (T, T, H), (T, H, T), (H, T, T), (T, T, T)} Let us define 3 events as E : 3 head or 3 tails F : atleast two heads G : atmost two heads E : 3 head or 3 tails E : {HHH, TTT} P(E) = 2/8 = 1/4 vF : atleast two heads F : {HHH, HHT, HTH, THH} P(F) = 4/8 = 1/2 G : atmost two heads G : {HHT, HTH, THH HTT, THT, TTH ,TTT } P(G) = 7/8 Finding probabilities of E, F and G Now, let us find Probabilities of E ∩ F , F ∩ G , E ∩ G E ∩ F = 3 head = {HHH} So, P(E ∩ F) = 1/8 Now, P(E) . P(F) = 1/4 × 1/2 = 1/8 P(E ∩ F) = P(E).P(F) Thus, E & F are independent events F ∩ G = Two head = {HHH, HTH, THH} So, P(F ∩ G) = 3/8 Now, P(F) . P(G) = 1/2 × 7/8 = 7/16 P (F ∩ G) ≠ P(F) . P(G) Thus, F & G are not independent events E ∩ G = 3 tails = {TTT} So, P(E ∩ G) = 1/8 Now, P(E) . P(G) = 1/4 × 7/8 = 7/32 P (E ∩𝐆) ≠ P (E). P(G) Thus, E & G are not independent events
Examples
Example 2
Example 3
Example 4
Example 5 Important
Example 6
Example 7 Important
Example 8
Example 9 Important
Example 10
Example 11 Important
Example 12 Important You are here
Example 13 Important
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Example 18 Important
Example 19 Important
Example 20 Important
Example 21 Important
Example 22
Example 23
Example 24 Important
Example 25 Important
Example 26 Important
Example 27 Not in Syllabus - CBSE Exams 2021
Example 28 Important Not in Syllabus - CBSE Exams 2021
Example 29 Important Not in Syllabus - CBSE Exams 2021
Example 30 Important Not in Syllabus - CBSE Exams 2021
Example 31 Important Not in Syllabus - CBSE Exams 2021
Example 32 Important Not in Syllabus - CBSE Exams 2021
Example 33 Important
Example 34 Important Not in Syllabus - CBSE Exams 2021
Example 35 Important
Example 36 Important
Example 37 Important
About the Author