Question

2 coins are tossed simultaneously. find probability of getting: 1)exactly one head 2)at least one tail 3) no tail 4) at most one head

Answer 1

When two coins are tossed the results can be like this (let us give numbers for them)

1) Both are heads i.e. HH

2) First head, then tail i.e. HT

3) First tail, then head i.e. TH

4) Both are tails i.e. TT

The total number of outcome is 4.

Find the probability of getting  

1) exactly one head: - Only cases 2 and 3 from the above chances qualify for this criteria. So probablity is 2/4 = 1/2

2) At least one tail: - Only cases 2, 3 and 4 from the above chances qualify for this criteria. So probablity is 3/4

3) No tail: - Only case 1 from the above chances qualify for this criteria. So probablity is 1/4

4) At most one head: - This means either no head or only one head. So cases 2,3 and 4 from the above chances qualify for this criteria. So probablity is 3/4

Answer 2

Step-by-step explanation:

(1) exactly one head

Total outcomes = (H,T),(T,H)

favourable outcomes/total no. of outcomes

2/4 = 1/2

(2) at least one tail

Total outcomes = (H,H),(H,T),(T,H)

favourable outcomes/total no. of outcomes

3/4 = 1/2

(3) no tail

Total outcomes = (H,H)

favourable outcomes/total no. of outcomes

1/2

(4) at most one head

Total outcomes = (T,T),(H,T),(T,H)

favourable outcomes/total no. of outcomes

3/4 = 1/2