Question

A probability experimentis conducted in which the sample space of the experimentis S =(2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13), event F = 15, 6, 7, 8, 9), and event G-19, 10, 11, 12). Assume that each outcome is equally likely List the outcomes in For G. Find PF or G) by counting the number of outcomes in For G. Determine P/F or G) using the general addition rule List the outcomes in For G. Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A FORGO (Use a comma to separate answers as needed) OB. For G=) Find PF or C) by counting the number of outcomes in For G. PIF or G)-0 (Type an integer or a decimal rounded to three decimal places as needed) Determine P/F of G) using the generation Select the correct choice below and fill in any answer boxed within your choice. (Type the terms of your expression in the same order as they appear in the original expression Round to three decimal places as needed) OA PIOG) OB. PIFOG)

Answer 1

• Here, F or G = { all the values in F and G ignoring the repitions if there are any}. So, the correct answer -

          A.  

•     The required probability -

        $P(F \ or \ G)=\frac{Number \ of \ values \ in \ \{F \ or \ G\}}{ Number \ of \ values \ in \ \{S\}}=\frac{8}{12}=0.667$ (answer)

• Using general addition rule, we get,

         

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

          Now,

         $P(F)=\frac{5}{12}=0.417 \ and \ P(G) =\frac{4}{12}=0.333$

          Also,   

          ( the commomn values of F and G sets)

{F and G} = {9}

          So,

         $P( F \ and \ G ) =\frac{1}{12}=0.083$

          Hence, the correct answer is :

         (answer)