An experiment consists of tossing 3 coins
∴ The sample space of the given experiment is given by
S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
∴ n(S) = 8
(i) Let E be the event that 3 heads appear
∴ n(E) = 1 (Since E = {HHH})
⇒ P (E) =

n(E)

n(S)

=

1

8

(ii) Let E be the event that 2 heads appear
∴ n(E) = 3 (Since E = {HHT, HTH, THH})
⇒ P (E) =

n(E)

n(S)

=

3

8

(iii) Let E be the event that atleast 2 heads appear
∴ n(E) = 4 (Since E = {HTH, HHT, THH, HHH})
⇒ P (E) =

n(E)

n(S)

=

4

8

=

1

2

(iv) Let E be the event that at most 2 heads appear
∴ n(E) = 7 [Since E = HHT, HTH, THH, TTT, THT, TTH, HTT]
⇒ P (E) =

n(E)

n(S)

=

7

8

(v) Let E be the event that no head appears
∴ n(E) = 1 (Since E = {TTT}) ⇒ P (E) =

n(E)

n(S)

=

1

8

(vi) Let E be the event that 3 tails appear
∴ n(E) = 1 (Since E = {TTT})
⇒ P (E) =

n(E)

n(S)

=

1

8

(vii) Let E be the event that exactly two tails appear
∴ n(E) = 3 (Since E = {TTH, THT, HTT})
⇒ P (E) =

n(E)

n(S)

=

3

8

(viii) Let E be the event that no tail appears
∴ n(E) = 1 (Since E = {HHH})
(ix) Let E be the event that atmost two tails appear
∴ n(E) = 7 (Since E = {THH, HTH, HHT, HTT, THT, TTH, HHH})
⇒ P (E) =

n(E)

n(S)

=

7

8