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={4, 5, 6, 7, 8}​, and event G={8, 9, 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. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

                                               

A. F or G =_________

​(Use a comma to separate answers as​ needed.)

B. F or G =_________

Answer 1

Solution:

Given sample space is:

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

Thus total outcomes in sample space S are = N = 12

Event F = {4, 5, 6, 7, 8}​, and

Event G={8, 9, 10, 11}.

Part a) List the outcomes in F or G.

F or G means all outcomes in F or in G or outcomes in both F and G.

Thus

Outcomes in F or G = { 4, 5, 6, 7, 8 , 9, 10, 11}​

Number of outcomes in F or G = 8

Part b) Find P(F or G) by counting the number of outcomes in F or G.

P(F or G) = Number of outcomes in F or G / Total outcomes in sample space S

P(F or G) = 8 / 12

P(F or G) = 2 / 3

P(F or G) = 0.6667

Part c) Find P(F or G) using the general addition rule.

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

where

P(F) = Number of outcomes in event F / N = 5 / 12

P(G) = Number of outcomes in event G / N = 4 / 12

and

P( F and G) = Number of outcomes in both event F and G / N = 1 / 12

There is only one outcome which is common to both events F and G which is 8.

Thus

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

P(F or G) = 5/12 + 4/12 - 1/12

P(F or G) = ( 5 + 4 - 1 ) /12

P(F or G) = 8 / 12

P(F or G) = 2 / 3

P(F or G) = 0.6667