Last lecture… An experiment is a process by which an observation is made. A random experiment is an experiment that can result in different outcomes, even though it is repeated in the same manner every time. The sample space of an experiment is the collection of all possible outcomes. An event is a set (collection) of one or more outcomes in the sample space. In other words, an event is any subset of sample space that satisfies the conditions specified in the description. An event occurs when the experiment results in an outcome belongs the event. Probability and related calculation.

Polycarbonate plastic are analyzed for scratch and shock resistance. Random experiment: for each plastic, we measure the scratch resistance and shock resistance. The resistance is either low or high, abbreviated as L or H. If the ordered pair LH (outcome) indicates that the plastic has low scratch and high shock resistance, then the sample space can be represented by: A)S = { LH, LL, HL, HH } B)S = { L, H } 3 4 A. This experiment has 4 possible outcomes.

Take 50 samples of polycarbonate plastic. Result is shown in a two-way table (Often used to visual two categorical variables) What is in blank (1) and (2)? A)(1) = 10, (2) = 6 B)(1) = 5, (2) = B. (1) = 6-1, (2) = Shock Resistance HighLowTotal Scratch Resistance High40444 Low1(1)6 Total41(2)50

Take 50 samples of polycarbonate plastic. Result is shown in a two-way table (Often used to visual two categorical variables) Let A denote the event that a sample has high shock resistance. let B denote the event that a sample has high scratch resistance. What is P(A) and P(B)? A)P(A) = 41/50, P(B) = 44/50 B)P(A) = 40/41, P(B) = 40/ A is correct. Shock Resistance HighLowTotal Scratch Resistance High40444 Low156 Total41950

Take 50 samples of polycarbonate plastic. Result is shown in a two-way table (Often used to visual two categorical variables) Let A denote the event that a sample has high shock resistance. let B denote the event that a sample has high scratch resistance. What is event A∩B and its probability ? A ) Samples for which scratch and shock resistances are high. P(A∩B) = 40/50 B ) Samples for which either scratch or shock resistances are high. P(A∩B) = 44/ A is correct. Shock Resistance HighLowTotal Scratch Resistance High40444 Low156 Total41950

Take 50 samples of polycarbonate plastic. Result is shown in a two-way table (Often used to visual two categorical variables) Let A denote the event that a sample has high shock resistance. let B denote the event that a sample has high scratch resistance. What is event A’ and its probability ? A) Samples in which the shock resistance is not high. P(A’) = 4/44 B) Samples in which the shock resistance is low. P(A’) = 9/ B is correct. Shock Resistance HighLowTotal Scratch Resistance High40444 Low156 Total41950

Conditional probability and Independent

Take 50 samples of polycarbonate plastic. Result is shown in a two-way table (Often used to visual two categorical variables) Find P( Low Scratch Resist.|High Shock Resist.). A) 4/44 B) 1/ B is correct. Shock Resistance HighLowTotal Scratch Resistance High40444 Low156 Total41950