Consider the experiment of tossing a coin. If the coin shows head, toss it again but if it shows tail then throw a die. Find the conditional probability of the event that the die shows a number greater than 4 given that there is at least one tail

Explanation

According to the equation, sample space
`S = {(H,H),(H,T),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}`
In the above set, there are 8 elementary events, but all are not equally likely.
However, events (H,H) and (H,T) are equally likely.
Each event has probability `(1)/(4)` (considering sample space `{HH, HT, TH, T T}`
Events (T, 1), (T, 2), ...,(T, 6) are also equally likely.
Let probability of each be p. Then
`6p = 1 - (1)/(4) - (1)/(4) = (1)/(2)`
`therefore p = (1)/(12)`
Let event A be ''the dice shows a number greater than 4'', and event B be ''there is at least one tail''.
`therefore A = {(T, 5),(T, 6)}`
`"and "B = {(H,T),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}`
`therefore P(A) = (1)/(12) + (1)/(12) = (1)/(6)`
`P(B) = (1)/(4) + (1)/(12) + (1)/(12) + (1)/(12) + (1)/(12) + (1)/(12) + (1)/(12)=
(1)/(4) + (1)/(2) = (3)/(4)`