A probability experiment is conducted in which the sample sp

A probability experiment is conducted in which the sample space of the experiment is S= (1,2,3,4,5,6,7,8,9,10,11,12), event F= (4, 5, 6, 8), and event G= (10, 11). Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.

Solution

Here,

F or G = {4,5,6,8,10,11} [ANSWER]

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Thus, as there are 12 outcomes in S, and only 6 in F or G,

P(F or G) = 6/12 = 1/2 OR 0.5 [ANSWER]

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F and G = { } [they do not intersect]

Thus,

P(F or G) = P(F) + P(G) - P(F and G)

= 4/12 + 2/12 - 0/12

= 1/2 [ANSWER]