Answer to Question #351045 in Statistics and Probability for Bob

Question

1. QUESTION:

Describe the sample space and all 16 events for a trial in which two coins are thrown and each shows either a head or a tail.

Answer 1

The sample space is $S=\{hh, ht, th, tt\}.$

As this has 4 elements there are $2^4=16$ subsets, namely

$$\empty,\{ hh\}, \{ht\}, \{th\}, \{tt\}, \{hh, ht\},\{hh, th\},$$ $$\{hh, tt\},\{ht, th\},\{ht, tt\},\{th, tt\},$$ $$\{hh, ht, th\}, \{hh, ht, tt\},\{hh, th, tt\},$$ $$\{ht, th, tt\},\{hh, ht, th, tt\}$$