MATH 2311 Section 2.4. General Probability Rules Two events are independent if knowing that one occurs does not change the probability that the other.

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Presentation transcript:

MATH 2311 Section 2.4

General Probability Rules Two events are independent if knowing that one occurs does not change the probability that the other occurs. (Note: This is not the same as sets that are disjoint or mutually exclusive)

Dependent Events

Examples: A clothing store that targets young customers (ages 18 through 22) wishes to determine whether the size of the purchase is related to the method of payment. A sample of 300 customers was analyzed and the information is below:

a.If a customer is selected at random from this group of customers, what is the probability that the customer paid cash? b. If a customer is selected at random from this group of customers, what is the probability that the customer paid with a credit card? c. If a customer is selected at random from this group of customers, what is the probability that the customer paid with the layaway plan?

d. If a customer is selected at random from this group of customers, what is the probability that the customer purchased under $40? e. If a customer is selected at random from this group of customers, what is the probability that the customer purchased $40 or more?

f. If a customer is selected at random from this group of customers, what is the probability that the customer paid with a credit card given that the purchase was under $40? g. If a customer is selected at random from this group of customers, what is the probability that the customer paid with the layaway plan given that the purchase was $40 or more?

Determine if events A and B are independent. Popper 2: (EMCF 2) A. IndependentB. Dependent

Examples: Thirty percent of the students at a local high school face a disciplinary action of some kind before they graduate. Of those “felony” students, 40% go on to college. Of the ones who do not face a disciplinary action, 60% go on to coll a.What is the probability that a randomly selected student both faced a disciplinary action and went on to college? b. What percent of the students from the high school go on to college? c. Show if events {faced disciplinary action} and {went to college} are independent or not.