In a game, the entry fee is of 5. The game consists of a tossing a coin 3 times. If one or two heads show. Sweta gets her entry fee back. If she throw 3 heads, she receives double the entry fees. Otherwise, she will lose. For tossing a coint three times, Find the probability that she
(i) Loses the entry fee.
(ii) gets double entry fee.
(iii) just gets her entry fee.

Explanation

Total possible outcomes of tossing a coin 3 times.
S={(HHH),(TTT),(HTT),(THT),(TTH),(THH),(HTH),(HHT)}
n(S)=8
(i) Let `E_(1)`=Event that Sweta losses the entry fee
=She tosses tail on three times
`n(E_(1))`={(TT)}
`P(E_(1))=(n(E_(1)))/(n(S))=(1)/(8)`
(ii) Let `E_(2)`=Event that Sweta gets double entry fee
=She tosses heads on three times={(HHH)}
`n(E_(2))=1`
`therefore P(E_(2))=(n(E_(2)))/(n(S))=(1)/(8)`
(iii) Let `E_(3)`= Event that Sweta gets her entry fee back
=Sweta gets heads one two times
={(HTT),(THT),(TTH),(HHT),(HTH),(THH)}
`therefore n(E_(3))=6`
`therefore P(E_(3))=(n(E_(3)))/(n(S))=(6)/(8)=(3)/(4)`