Answer to Question #351001 in Statistics and Probability for EDD

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

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

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

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

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