Test exact independence
A finite sample space S contains 20 coded samples. One outcome is selected uniformly, so all individual outcomes are equally likely
Use the notation \(\Pr(A)\), \(\Pr(B)\) and \(\Pr(A\cap B)\)
Event A is the condition that the outcome has a short code; event B is the condition that the outcome is placed in the blue bin
The finite sample space is listed below. The events are subsets of S
\[S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}\]
\[A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}\]
\[B = \{1, 2, 13, 14, 15\}\]
Use the exact values to decide whether events A and B are independent