stat 2 test review - Probability Probability is the...

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Probability Probability is the likelihood of a particular outcome occurring. Example: probability of drawing a club from a deck of cards Example: in an urn full of 10 red marbles and 12 black marbles, the probability of drawing a black marble is p = 12 10 + 12 = 12 22 Law of Large Numbers • As we repeat an experiment a large number of times, the ratio of the number of successes in the sample to the total number of trials will approach the probability of the event. • Example: proportion of heads should go to .5 10 coins: 7 H 3 T p = .7 100 coins: 53 H 47 T p = .53 1000 coins: 498 H 502 T p = .498 10000 coins: 5002 H 4998 T p = .5002 Types of Probabilities • Classical/Relative Frequency • Subjective – Likelihood of an event is based on your own personal judgment Probability Definitions • A complement – All possible events that are not in A • Example: – A = it’s snowing – A c = it’s not snowing Example of a Complement We have a total of 50 seats in a room, and a shaded square above represents a taken seat. How many people are in this room? It’s easier to instead count the number of empty seats, of which there are 4. Therefore the number of people is 50 - 4 = 46 So the complement here is “all empty seats” which gives us the needed answer more easily. Probability (HW 5.1-5.3) The game Scrabble contains 100 lettered tiles: 56 consonants, 42 vowels, and 2 blanks. The 42 vowels can be further classified as follows: 9 A’s, 12 E’s, 9 I’s, 8 O’s, and 4 U’s. Suppose we reach into a bag containing all the tiles and select one letter. What’s the probability of drawing a tile with a letter on it? 98 such tiles, so 98/100 = .98 If we draw a vowel, what’s the probability it’s in the upper half of the alphabet? (Meaning A - M) Out of 42 vowels, the A’s, E’s, and I’s count, so If the tile drawn contains a letter on it, what’s the probability that letter is not a vowel? Out of 98 letters, 56 of them are not vowels. 9 + 12 + 9 42 = 30 42 = .714285 56 98 = .57143
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Probability (HW 5.1-5.3) We have an urn full of marbles of the following colors: 5 green, 4 blue, 3 yellow, 2 red, 1 white (15 total). What’s the probability of drawing a primary color? (Red, yellow, or blue) If the marble drawn was a primary color, what’s the probability it was either red or yellow? Out of 9 primary color marbles, we have 2 red and 3 yellow, so If the marble drawn was not a primary color, what’s the probability it was not green? 2 + 3 + 4 15 = 9 15 = .6 2 + 3 9 = 5 9 = .55556 There are 6 non-primary color marbles: 5 green, 1 white. So, out of 6 marbles, 1 is not green (the white). 1 6 = .16667 Probability (HW 5.1-5.3) The ice cream HW question again! Find the probability that an individual selected is female and prefers strawberry ice cream. Out of all 2176, we have 302 that are both female and like strawberry, so 302 / 2176 = .13879 Find the probability that an individual selected is female or prefers strawberry ice cream. Out of 2176 again. We count the number who are either female or like strawberry, or both. (As long as they have at least one of the two characteristics, we count them.) As indicated above, this
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stat 2 test review - Probability Probability is the...

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