Question

Question 4 Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”. C denote the event “three tails show” and D denote the event ‘a head shows on the first coin”. Which events are

(i) mutually exclusive? (ii) simple? (iii) compound?

Class X1 - Maths -Probability Page 393

Answer 1

when three coins are tossed , then total number of possible outcomes = 2³ = 8
S = { (HHH), (HHT),(HTT),(TTT),(THH),(TTH),(THT),(HTH)}

Now,
A = three heads shows = {(HHH)}
B = two heads and one tails = {(HHT),(THH),(HTH)}
C = three tails shows = {(TTT)}
D = A head shows on the first toss = {(HHH),(HHT),(HTT),(HTH)}

we see ,
A ∩ B = Φ
A ∩ C = Φ
B ∩ C = Φ
C ∩ D =Φ
A ∩ B ∩ C = Φ

hence, A and B , A and C , B and C , C and D and A, B and C are mutually exclusive .

(ii) see set of A, B , C and D .
we observed only A , C have one simple point
e.g., A = {(HHH)} , B = {(TTT)}
so, A and C are simple events.

(iii) B and D have more than two simple points
e.g., B = {(HHT),(HTH),(THH)}, D ={(HHH),(HHT),(HTH),(HTT)}
so, B and D are compound events .