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# 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

**Solution:**

A die has six faces that are numbered from 1 to 6. When a die is rolled, the possible outcomes are {1, 2, 3, 4, 5, 6}.

If the number on the die is even (i.e., if we get 2, 4, (or) 6), then the coin is tossed. Then the possible outcomes are {2H, 2T, 4H, 4T, 6H, 6T}.

If the number on the die is odd (i.e., if we get 1, 3, (or), 5), the coin is tossed twice. Then the possible outcomes are {1HH, 1HT, 1TH, 1TT, 3HH, 3HT, 3TH, 3TT, 5HH, 5HT, 5TH, 5TT}

Hence, the sample space of this experiment is given by:

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

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.1 Question 14

## 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.

**Summary:**

The sample space for the experiment(S) = {1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T}

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