Introduction to probability (4) Theorems:
Introduction to probability (4) Example: Two dice are tossed; find the probability of getting an even number on the first die or a total number of 8. Solution: A: Getting an even number on the first die. B: The sum of the options obtained on the two dice 8.
Introduction to probability (4)
Introduction to probability (4) Example: If the probability that an automobile machine will serve 3, 4, 5, 6, 7 or 8 or more cars on any given workday are respectively: 0.12, 0.19, 0.28, 0.24, 0.10 and 0.07. What is the probability that it will be serve at least 5 cars on next day at work. Solution: Let E be the event that at least 5 cars are served
Introduction to probability (4)
Conditional Probability The probability of an event B occurring when it is known that some event A has occurred is called a conditional probability and is denoted by and it can pronounced as “ The probability of B given A”.
Conditional Probability Example: B is an event of getting a perfect square when a die is tossed the die is constructed so that the even numbers are twice as likely to occur as the odd numbers. Find the probability that B occurs relative to the space A and A is the number greater 3.
Conditional Probability Solution:
Conditional Probability Definition: By the above definition we can solve the above question by another way as:
Conditional Probability Example: Employed Unemployed Total Male 460 40 500 Female 140 260 400 600 300 900 If we select one person from above table and the event is: M: a man is chosen. E: the once chosen is employed
Conditional Probability Solution: We can solve the above problem by two methods as: Directly from table as:
Conditional Probability 2. Or
Conditional Probability Example: The listed table is the number of contaminated wafer: No. Cont. Center Edge Total 0.3 0.1 0.4 1 0.15 0.05 0.2 2 3 0.06 0.04 4 0.01 5 and more 0.07 0.03 0.72 0.28
Conditional Probability Assume that one wafer is selected at random from this set let A denotes the event that a wafer contains four or more particles and let B denotes the event that a wafer is from a center. Find:
Conditional Probability
Conditional Probability