basic probabilty

basic probabilty

1. A Sample Space

   • all possible outcomes of an event
   • Size of Sample Space
     • Size of S = the number of outcomes.
   • The General Case
     • S = (n1)(n2)(n3)…(nk) where n=outcomes per step, and k=steps
   • Combinations
     • order is not important How many combinations are there of three items selected from a group of six items? Three chosen from six is 6! / (3!)(3!) = (6x5x4)/(3x2x1) = 20
     • Size of Sample Space for Combinations
   • Permutations
     • order is important How many permutations are there of three items selected from a group of six items? Permutations: 6!/(6-3)! = 6!/3! = 6x5x4 = 120  

2. The Basics of Probability

   • Probability of a Single Event
     • a mathematical statement of the likelihood of an event occurring. Probabilities range from 0 to 1. There are 32 products in a box.  4 of them are defective.  What is the probability of drawing a defective item? 4/32 = .125
   • Probability of the Complement of an Event
     • :   the event does not occur. Probability of X not occurring is P(XC). Since an event either occurs, or it doesn’t, P(X) + P(XC) = 1   There are 40 students in a class.  18 of them are women.  What is the probability of not choosing a woman? P(W)=18/40 = .45, so P(not a woman) = .55

3. Joint Probability

   • Probability of Union of Two Events
     • The Union of Events is Event X  or  Event Y occurring. :  A warehouse has 18,000 steel rods in inventory, of various lengths and widths. 4000 of the rods are 6 meters long, 7000 of them are 2.5 cm wide, and 1500 of them are 6 metres long and 2.5 cm wide.  A contractor has two job offers today: one job requires a rod of 6 metres, and the other job requires a 2.5 cm rod. If he randomly selects a rod, what is the probability that he will get some work done today? P(six metres) = 4000/18000 = .2222    and P(2.5 cm) = 7000/18000 = .3889    and P(of a 6 m, 2.5 cm rod) = 1500/18000 = .0833.  P(X union Y) = .2222 + .3889  - .0833 = .5278
   • Probability of Intersection of Two Events (Independent and Mutually Exclusive)
   • Joint Probability Tables

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