Question

Shubendhu rolls a dice. If he obtains a prime number, he tosses a coin and if he gets an even number, he rolls a dice again. What is the cardinality of the sample space?

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Answer 1

Possible outcomes when Shubendhu rolls a dice is 1, 2, 3, 4, 5 and 6

Possible prime number outcomes are 2, 3 and 5

Possible even number outcomes are 2, 4 and 6

2 is an even prime. Therefore, Shubendhu has to toss a coin as well as roll a dice.

Let H and T represent head and tail while tossing a coin.

Therefore, sample space S = {(1), (2, 1, H), (2, 2, H), (2, 3, H), (2, 4, H), (2, 5, H), (2, 6, H), (2, 1, T), (2, 2, T), (2, 3, T), (2, 4, T), (2, 5, T), (2, 6, T), (3, H), (3, T), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, H), (5, T), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(S) = 29.