Question

 Three coins are tossed. What is the probability of getting 

(i) all heads, 

(ii) two heads, 

(iii) at least one head, 

(iv) at least two heads?

Answer 1

Let ‘S’ be the sample – space. Then S = { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT } 

(i) Let ‘E1’ = Event of getting all heads, Then E1 = { HHH } 

 |E1| = 1 

 P(E1) = |E1| / |S| = 1 / 8 

(ii) Let E2 = Event of getting ‘2’ heads. Then: 

 E2 = { HHT, HTH, THH } 

 |E2| = 3 P (E2) = 3 / 8 

(iii) Let E3 = Event of getting at least one head. Then: 

 E3 = { HHH, HHT, HTH, THH, HTT, THT, TTH } 

 |E3| = 7 

 P (E3) = 7 / 8 

(iv) Let E4 = Event of getting at least one head, Then: 

 E4 = { HHH, HHT, HTH, THH, } 

 |E4| = 4 P 

(E4) = 4/8 = 1/2