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}