Example 12 - Chapter 13 Class 12 Probability
Last updated at April 16, 2024 by Teachoo
Independent events
Ex 13.2, 6
Ex 13.2, 10 Important
Ex 13.2, 5
Example 10
Example 11 Important
Example 12 Important You are here
Ex 13.2, 15 (i)
Ex 13.2, 8
Ex 13.2, 7 Important
Ex 13.2, 11 (i)
Ex 13.2, 4
Ex 13.2, 13 Important
Ex 13.2, 14 Important
Ex 13.2, 18 (MCQ) Important
Example 13 Important
Example 14 Important
Independent events
Last updated at April 16, 2024 by Teachoo
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? 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)} Given 3 events as E : 3 head or 3 tails F : atleast two heads G : atmost two heads Finding probabilities of E, F and G Event E E : 3 head or 3 tails E = {HHH, TTT} P(E) = 2/8 = 1/4 Event F F : atleast two heads F = {HHH, HHT, HTH, THH} P(F) = 4/8 = 1/2 Event G G : atmost two heads G ={HHT, HTH, THH HTT, THT, TTH ,TTT } P(G) = 7/8 Now, let us find Probabilities of E ∩ F , F ∩ G , E ∩ G E and F E ∩ F = {HHH} So, P(E ∩ F) = 1/8 Now, P(E) . P(F) = 1/4 × 1/2 = 1/8 = P(E ∩ F) P(E ∩ F) = P(E).P(F) Thus, E & F are independent events F and G F ∩ G = {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 and G E ∩ G = {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