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, 7}, 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.

List the outcomes in F or G. Choose the correct answer below.

a) F or G= {4, 5, 6, 7}

b) F or G= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

c) F or G= {10, 11}

d) F or G= {4, 5, 6, 7, 10, 11}

Find P(F or G) by counting the number of outcomes in F or G:

P(F or G)=

Determined P(F or G) using the general addition rule:

P(F or G)=

Solution

Outcomes in F or G

F ={4,5,6,7}

G = {10,11}

F or G={4,5,6,7,10,11}

P(F or G) = n(F or G)/n(s)

               = 6/12

               = 1/2

               = 0.5

therefore P(F or G) = 0.5

The general addition rule of P(F or G)

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

               = n(F)/n(S)+n(G)/n(S)-n(F andG)/n(S)

               = 4/12+2/12-0/12

               = 6/12

               = 1/2

               = 0.5

   Therefore the general addition rule of P(F or G) is 0.5