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# Concepts of Statistics STAT 135

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This 3 page Class Notes was uploaded by Floy Kub on Thursday October 22, 2015. The Class Notes belongs to STAT 135 at University of California - Berkeley taught by Staff in Fall. Since its upload, it has received 23 views. For similar materials see /class/226732/stat-135-university-of-california-berkeley in Statistics at University of California - Berkeley.

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Date Created: 10/22/15

Discrete probability review Here are a few handy techniques for computing probabilities 0 List all of the possible outcomes in the space7 which we call Omega If the outcomes are equally likely then A P A 7 lt gt 9 0 Use symmetry 0 Eliminate extra details7 and reduce the problem to an equivalent one 0 Consider nding the probability of the complement of the event of interest Let7s use these techniques to answer some questions about drawing cards from a well shuffled deck of playing cards Recall there are 52 cards in the deck7 13 red Hearts marked 2 through 107 J7 Q7 K7 A 13 red Diamonds 13 black Spades and 13 black Clubs Suppose we are interested in nding the probability for the following events A first card drawn is black B second card drawn is black 0 at least one A is drawn To nd PA we can list all of the possible outcomes To nd PB we can use symmetry PB Psecond card is red PB0 To nd the probability of 0 use the complement rule To do this7 list the outcomes as ordered pairs 1 draw7 2quotd draw Then 9 52 gtk 51 2652 and 00 48 gtk 47 2256 So 130 is 17 225626511493 Cons ider the following problems Suppose 5 cards are drawn from the top of the deck Find the chance that the ace of diamonds was drawn Find the chance that the ace of diamonds and the 2 of diamonds were drawn Find the chance that the rst card drawn was the Ace of diamonds the second was the 2 of diamonds the third drawn was the 3 of diamonds the fourth was the 4 and the fth was the 5 of diamonds Find the chance that the ve cards are the 2 3 4 5 and 6 of diamonds in any order Find the chance that 3 of the cards are red Simple Random Sampling Now lets transfer what you have know about drawing card from a deck to simple random sampling Deck of cards Cards are marked A K Shuffle the deck Dea Dea The The Cons class Stat 135 class Students are ordered 1 N 70 in our case Randomize the order of the students Pick a student from the class Select a sample of 71 students The chance the rst student chosen is 1 The number of distinct samples drawn 1 a card from the deck 1 71 cards from the deck chance the Ace of diamonds is picked number of possible hands77 dealt ider the following problems Suppose 5 students are chosen at random from the Find the chance that student 37 was chosen 7 Find the Chance that 37 and 38 were in the sample 7 Find the Chance that the rst student selected for the sample was 1 the second was 2 and the the fth was student 5 7 Find the Chance that the ve students in the sample are 1 2 3 4 5 7 Find the Chance that 3 of the students have spans larger than 20 cm 7 Hang on rst we need the following information Here are the right hand spans in cm of the students in our Class Span cm Count 17 18 185 19 195 D H H HawiboowcwH to co ww qgt w Consider our Class as a population Make a histogram of the population values for hand span

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