Question

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice.
Write the sample space for this experiment.

Answer 1

When a die is rolled then

$S_1$ = {1, 2, 3, 4, 5, 6}

When even number is turns up on the face then a coin is tossed

$\therefore S_2$ = {(2, H), (2, T), (4, H), (4, T), (6, H). (6, T)}

Whereas when odd number turns up then coin is tossed two times

$\therefore S_3$ = {(1, HH), (I, HT), (1, TH), (1, TT), (3, HH), (3, HT), (3, TH),(3, TT),(5, HH), (5, HT), (5, TT)}

$\therefore$ Sample space associated with this experiment is
$S=[S_2\cup S_3]$

S ={(2, H), (2, T), (4, H), (4, T),(6, H),(6, T),
(1, HH), (1, HT), (1, TH), (1, TT),
(3, HH), (3, HT), (3, TH), (3, TT),
(5, HH), (5, HT), (5, TH), (5, TT)}