Question

A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number the die is thrown again. What is the sample space for the experiment?

Hint: Sample space is a set which contains all possible outcomes of a random experiment. Tossing coins, rolling dice, picking a card all are such experiments.

When we toss a coin we will get either a head or a tail. Let’s represent the head with H and tail with
T. The possible numbers that can appear on die are 1, 2, 3, 4, 5 and 6.
Here our experiment is we toss a coin, if it shows ‘H’ we roll a die, if the number on the die is even
we roll the die again.
$\therefore$ Sample space S = { T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44,
H45, H46, H61, H62, H63, H64, H65, H66}

Our sample space consists of 22 elements.

Note: For the first time when we toss a coin, if the coin shows ‘T’ we will stop there. If the coin shows up
‘H’, we will continue the experiment to roll a die. If the number on the die is odd we stop our experiment there itself. If the number on the die is even, we roll it again, completing our experiment.
H1 represents head on coin, 1 on rolling die for the first time. Odd number on die. So we stopped there. H25 represents head on coin, 2 on rolling die for the first time, even number on die so we roll the die
for the second time. The number 5 appeared on rolling the die for the second time.
Experiment completed.