Chapter 6 Section 2 Experiments, Outcomes, and Events

Basic Definitions Experiment: An activity with an observable outcome. Trial:The act of performing a single experiment. Outcome:The observable result of the experiment.

Sample Space (S) Sample Space: –The set of all possible outcomes of the experiment. –Set should be chosen so that there is no overlap –S = { ‘list of all possible outcomes’ } You can think of the sample space as the universal set for the experiments.

Events Event: A set that is a subset of the sample space. Impossible Event:An event that cannot occur. –i.e. The outcome is not in the sample space. –Denoted using the symbol: Ø

Exercise 5 (page 270) Situation:Two urns, each containing several balls. Both urns contain some red balls and some white balls. Urn I ? ? ? ? ? ? ? ? ? ? ? ? Urn II

Exercise 5 Notation Definition Let : 1.I represent Urn I 2.II represent Urn II 3.R represent a Red Ball 4.W represent a White Ball Experiment: Pick one of the two urns and then draw a ball from the urn that is picked.

Exercise 5 Part (a) What is a suitable sample space for this experiment? Possible Solution: S = { ( I, R ), ( I, W ), ( II, R ), ( II, W) }

Exercise 5 Part (b) Describe the event “Urn I is selected” E = { ( I, R ), ( I, W ) }

For events E and F The event E  F occurs precisely when either event E or event F (or both) occur. The event E  F occurs precisely when both events E and event F occur.

Other relationships: Event E occurs when event E does not occur. E  E = S E  E =  Two events are mutually exclusive (or disjoint) events when: E  F = 

Exercise 7 (page 270) Efficiency expert records the time that it takes an assembly line worker to perform a particular task. Let event… E = { more than five minutes } F = { less than eight minutes } G = { less than four minutes }

Exercise 7 (part a) Describe the sample space for this experiment. S = { all positive numbers of minutes }

Exercise 7 (part b) Describe the following: 1.E  F E  F = { more than 5 minutes but less than 8 minutes } 2.E  G E  G =  3.E E = { 5 minutes or less }

Exercise 7 (part b) continued Describe the following: 4.E  F E  F = {5 minutes or less } 5.E  F  G E  F  G = { less than 4 minutes } 6. E  F E  F = S

Exercise 17 (page 271) Toss a coin 10 times and observe the number of heads. (a)Sample space? S = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } (b)Describe the event E of “more than 5 heads” in terms of the sample space. E = { 6, 7, 8, 9, 10 }

Exercise 3(page 270 ) Toss a coin twice and observe the sequence of heads (H) and tails (T). (a)Define the sample space: S = { HH, HT, TH, TT } (b)The first toss is a head: E = { HH, HT}