# Example 12 - Chapter 13 Class 12 Probability (Term 2)

Last updated at Feb. 15, 2020 by 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 1

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 Deleted for CBSE Board 2022 Exams

Example 28 Important Deleted for CBSE Board 2022 Exams

Example 29 Important Deleted for CBSE Board 2022 Exams

Example 30 Important Deleted for CBSE Board 2022 Exams

Example 31 Important Deleted for CBSE Board 2022 Exams

Example 32 Important Deleted for CBSE Board 2022 Exams

Example 33 Important

Example 34 Important Deleted for CBSE Board 2022 Exams

Example 35 Important Deleted for CBSE Board 2022 Exams

Example 36 Important

Example 37 Important

Chapter 13 Class 12 Probability (Term 2)

Serial order wise

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.