A coin is tossed. If the outcome is the 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?

Solution:

When a coin is tossed, the possible outcomes are head (H) and tail (T). So the sample space corresponding to "coin is tossed" is {H, T}.

If the outcome is head, a die is thrown. When a die is thrown, the possible outcomes are 1, 2,3, 4,5 or 6. Thus, the corresponding sample space is, {H1, H2, H3, H4, H5, H6}.

If the die shows up an even number, a die is thrown again. The corresponding sample space is {H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H46, H61, H62, H63, H64, H65, H66}.

Thus, the sample space of the given experiment is

S = {T, H1, H2, H3, H4, H5, H6, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H46, H61, H62, H63, H64, H65, H66}

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.1 Question 12

A coin is tossed. If the outcome is the 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?

Summary:

The sample space for the experiment, S = {T, H1, H2, H3, H4, H5, H6, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H46, H61, H62, H63, H64, H65, H66}