STAT 400 Lecture 5: Conditional Probability and Total Probability(Revised)

• School: University of Maryland
• Department: Statistics and Probability
• Course: STAT 400
• Professor: Natalia Tchetcherina

Document Summary

N=5, k=5: n times? (cid:884, coin tossed 10 times? (cid:884)(cid:2869)(cid:2868) (cid:4666)(cid:2873) (cid:2873)(cid:4667)!=(cid:887)! (cid:2873)! 5*5*5*5*5=(cid:887)(cid:2873) (cid:1842)(cid:2872),(cid:2871)(cid:2868)= (cid:2871)(cid:2868)! (cid:4666)(cid:2871)(cid:2868) (cid:2872)(cid:4667)!=(cid:2871)(cid:2868)! (cid:2870)(cid:2874)! (cid:4672)(cid:883)(cid:882)(cid:882)(cid:885)(cid:4673)(cid:4672)(cid:891)(cid:889)(cid:884)(cid:4673: a club has 30 members. In many experiments, we need to record the value of more than one characteristic from each population unit. When the characteristics depend on each other, we can use conditional probability. The probability of event a given event b is given by (cid:1842)(cid:4666)(cid:1827)|(cid:1828)(cid:4667) and is equal to: (cid:1842)(cid:4666)(cid:1827)|(cid:1828)(cid:4667)=(cid:1842)(cid:4666)(cid:1827) (cid:1828)(cid:4667) (cid:1842)(cid:4666)(cid:1828)(cid:4667) Ex: the following table shows the results of tests of defective batteries that are both old and new. 1 (cid:1842)(cid:4666)(cid:1867)(cid:1856)(cid:4667)= 8(cid:2869)8 (cid:1842)(cid:4666)(cid:1867)(cid:1856)|(cid:1857)(cid:1858)(cid:1857)(cid:1855)(cid:1872)(cid:1857)(cid:4667)=(cid:2870)(cid:2871: we have 52 cards and we take 5 of them at random. What is (cid:1842)(cid:4666)(cid:887) (cid:1855)(cid:1870)(cid:1856) (cid:1857)(cid:1870)(cid:1872)(cid:1871)|(cid:886) (cid:1855)(cid:1870)(cid:1856) (cid:1857)(cid:1870)(cid:1872)(cid:1871)(cid:4667)? (cid:1842)(cid:4666)(cid:887) (cid:1857)(cid:1870)(cid:1872)(cid:1871)(cid:4667) (cid:1842)(cid:4666)(cid:886) (cid:1857)(cid:1870)(cid:1872)(cid:1871)(cid:4667) (cid:1842)(cid:4666)(cid:886) (cid:1857)(cid:1870)(cid:1872)(cid:1871)(cid:4667)=(cid:4672)(cid:883)(cid:885)(cid:887)(cid:4673) (cid:4672)(cid:887)(cid:884)(cid:887)(cid:4673) (cid:4672)(cid:887)(cid:884)(cid:886)(cid:4673) Ex: 40% of bean seeds come from supplier a and 60% from supplier b. Seeds from supplier a have a 50% chance of germinating and seeds from b have a 75% chance of germinating.