A probability experiment is conducted in which the sample space of the experimen

Question

A probability experiment is conducted in which the sample space of the experiment is $ = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], event F = [3, 4, 5, 7], and event G = [9, 10, 11, 12]. 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. List the outcomes. In F or G Choose the correct answer bellow. A. F or G = [3, 4, 5, 7, 9, 10, 11, 12] B. F or G = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] C. F or G = [9, 10, 11, 12] D. F or G = [3, 4, 5, 7] Find P(F or G) by counting the number of outcomes in F or G. P(F or G) = 2/3 (Type an integer of a simplified fraction). Determine P(F or G) using the general addition rule. P(F or G) = ____ (Type an integer of a simplified fraction.)

Explanation / Answer

General addition rule is,

P( A or B ) = P( A ) + P( B )

S ={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

F = { 3, 4, 5, 7 }   ,      P( F) = 4/12

G = { 9,10,11,12 },       P(G) = 4/12

P( F or G ) = P( F ) + P(G )       ( Using general addition rule )

                  = 4/12 + 4/12

                  = 8/12 = 2/3

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