You roll an ordinary six-sided die. If you roll a “one” on the die, you toss a coin five times; if you roll a “two” on the die, you toss a coin six times. [In all other cases, you stop the experiment after rolling the die.] What is the size of the sample space?

When a die is rolled and we get one, the coin is tossed 5 times. Number of events that occur when a coin is tossed 5 times is $$ 2^5=32 $$ When a die is rolled and we get two, the coin is tossed 6 times. Number of events that occur when a coin is tossed 6 times is $$ 2^6=64 $$ and there are 4 other events where we stop the experiment .i.e when we get 3 or 4 or 5 or 6 Hence, the total number of events are $$ 32+64+4=100 $$ Hence, the size of the sample space is $$ 100 $$