Question

Question 5 Three coins are tossed. Describe

(i) Two events which are mutually exclusive.

(ii) Three events which are mutually exclusive and exhaustive.

(iii) Two events, which are not mutually exclusive.

(iv) Two events which are mutually exclusive but not exhaustive.

(v) Three events which are mutually exclusive but not exhaustive.

Class X1 - Maths -Probability Page 393

Answer 1

three coins are tossed ,
then total number of possible outcomes = 2³ = 8
Let A is the event of getting only heads
A = (HHH)
B is the event getting only tails
B = ( TTT)
here, A ∩ B = Φ
hence , A and B are mutually exclusive .

(ii) Let A is the event getting at least one tail .
A = {(THH),(TTH),(TTT),(HTH),(HHT),(THT),(HTT)}
B is the event getting only heads
B = (HHH)
so, A U B = S
and A ∩ B = Φ
so, A and B are mutually exclusive and exhaustive .


(iii) Let A is the event getting at least two heads
A = {(HHH),(HHT),(THH),(HTH)}
B is the event getting at no any tails
B = {(HHH)}
A ∩ B = { (HHH)} ≠ Φ
hence, A and B are not mutually exclusive.

(iv) same explanation like question (iii)

(v) Let
A = {(TTT)}
B = {(HHH)}
C = {(HTH)}
then,
A ∩ B ∩ C = Φ
and A ∪ B ∪ C ≠ S
hence, A , B and C are mutually exclusive but not exhaustive.