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Probability
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Sample Space: is the set of all possible outcomes
Example: rolling dice sample space = {1, 2, 3, 4, 5, 6} flipping a coin sample space = { H, T} Find the sample space of flipping a coin and rolling a dice. How many outcomes are in the sample space? Flip a coin Heads Tails Roll the dice 1 2 3 4 5 6 1 2 3 4 5 6 Sample space = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6} There are 12 possible outcomes when you flip a coin then roll a die
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Sample Space Example: Your choice of school clothes: Shirt: blue, white, black Bottoms: blk pants, tan pants, tan shorts, blk shorts Socks: red, blue, black, tan, white How many days in a row could you come to school with a different outfit? Sample space: There are 60 different outfits you could wear to school, which would cover 3 full months before having to repeat an outfit! Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts White Shirt Black Shirt Blue Shirt Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan
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Sample Space Example: Your choice of school clothes: Shirt: blue, white, black Bottoms: blk pants, tan pants, tan shorts, blk shorts Socks: red, blue, black, tan, white How many days in a row could you come to school with a different outfit? Sample space: What is the probability of a white shirt, black pants, and any color socks P(White shirt, Black pants, and any color socks) = ๐๐ข๐ก๐๐๐ก๐ = 1 12 or it means you have a 1 in 12 chance of picking out a White shirt, Black pants, and any color socks. Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts White Shirt Black Shirt Blue Shirt Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan
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Sample Space Example: Your choice of school clothes: Shirt: blue, white, black Bottoms: blk pants, tan pants, tan shorts, blk shorts Socks: red, blue, black, tan, white How many days in a row could you come to school with a different outfit? Sample space: What are the probability of wearing a black shirt, and blue socks? Probability = = 1 15 Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts White Shirt Black Shirt Blue Shirt Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan
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Probability of an event:
P(event) = ๐คโ๐๐ก ๐ฆ๐๐ข ๐ค๐๐๐ก ๐ก๐๐ก๐๐ ๐๐๐ ๐ ๐๐๐๐๐๐ก๐๐๐ Is the measure of the likelihood or chance that the event will occur. It can be expressed as a decimal, fraction, or percent. The chance of something happening is a number between zero and 1. Example: What is the probability of serving potatoes this week for lunch? The chance of zero means it will never happen Example: What is the probability the moon is made of green cheese? The chance of one means it will always happen Example: What is the probability of the sun rising tomorrow morning? P= P= P= P= P=1 Impossible unlikely equally could likely certain happen or not
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Calculating Probability:
You have 3 blue marbles, 5 yellow marbles, and 4 green marbles in a bag. What is the probability of picking a green marble from the bag? P(green) = 4 ๐๐๐๐๐ = = ๐ ๐ one in three chance of getting a green marble. What is the probability of getting a blue or a yellow marble? P(3 blue +5 yellow) = = = ๐ ๐ What is the probability of getting a black marble? P(black) = = =0; ๐กโ๐๐ ๐๐๐๐๐ ๐๐ก ๐๐ ๐๐๐ก ๐๐๐ ๐ ๐๐๐๐ ๐ก๐ ๐๐๐๐ ๐ ๐๐๐๐๐ ๐๐๐๐๐๐ ๐๐๐๐ ๐กโ๐ ๐๐๐. What is the probability of getting a blue or yellow or green marble? P(3 blue + 5 yellow + 4 green) = = = 1; ๐คโ๐๐โ ๐๐๐๐๐ ๐๐ก ๐ค๐๐๐ ๐๐๐ค๐๐ฆ๐ โ๐๐๐๐๐๐
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Example: P(blue) = 20 ๐๐๐ข๐ 62 ๐ก๐๐ก๐๐ ๐ โ๐๐๐ก๐ = 10 31
You and your friend designed T-shirts with silk-screened writing and are selling the T-shirts to raise money for the Speech Team. The table below shows the number of shirts in each design. Shirt Football logo Basketball logo Blue 10 White 8 12 Grey 16 6 What is the probability of a student choosing a T-shirt that is blue? What is the probability of choosing a white basketball shirt? What is the probability of choosing a football shirt? P(blue) = 20 ๐๐๐ข๐ 62 ๐ก๐๐ก๐๐ ๐ โ๐๐๐ก๐ = P(white basketball) = 12 ๐คโ๐๐ก๐ ๐๐๐ ๐๐๐ก๐๐๐๐ 62 ๐ก๐๐ก๐๐ = 6 31 P(football) = 34 ๐๐๐๐ก๐๐๐๐ 62 ๐ก๐๐ก๐๐ =
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Odds in favor and Odds against
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Odds in favor = ๐คโ๐๐ก ๐ฆ๐๐ข ๐ค๐๐๐ก ๐คโ๐๐ก ๐ฆ๐๐ข ๐๐ ๐ โฒ ๐ก ๐ค๐๐๐ก ; Odds against = ๐คโ๐๐ก ๐ฆ๐๐ข ๐๐ ๐ โฒ ๐ก ๐ค๐๐๐ก ๐คโ๐๐ก ๐ฆ๐๐ข ๐ค๐๐๐ก You have 3 blue marbles, 5 yellow marbles, and 4 green marbles in a bag. What are the odds of picking a green marble from the bag? Odds (green) = 4 ๐๐๐๐๐ 3 ๐๐๐ข๐+5 ๐ฆ๐๐๐๐๐ค What are the odds of not getting a blue marble? Odds (against blue) = 4 ๐๐๐๐๐ +5 ๐ฆ๐๐๐๐๐ค 3 ๐๐๐ข๐ = = or 50% = = 3 to 1 or 300%
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Spinner Example: If each section of the circle is the same size and just as likely to be chosen: Find P(purple) = Find P(even number) = Find P(multiple of 3 or red) = Find P(multiple of 5 and yellow) = Find P(prime number) = What are the odds in favor of landing on blue? What are the odds against landing on red? 2 ๐๐ข๐๐๐๐ 8 ๐ก๐๐ก๐๐ = 1 4 4 ๐๐ฃ๐๐ #๐ 8 ๐ก๐๐ก๐๐ = 1 2 3, 6, ๐๐๐ 8 ๐ก๐๐ก๐๐ = 3 8 0 ๐ฆ๐๐๐๐๐ค ๐๐ข๐๐ก๐๐๐๐๐ ๐๐ ๐๐๐ฃ๐ 8 ๐ก๐๐ก๐๐ = 0 2, 3, 5, 7 8 ๐ก๐๐ก๐๐ = = 1 2 3 ๐๐๐ข๐ 5 ๐๐๐ก ๐๐๐ข๐ = 3 5 7 ๐๐๐ก ๐๐๐ 1 ๐๐๐ = 7 1
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Sample Space Example: Your choice of school clothes: Shirt: blue, white, black Bottoms: blk pants, tan pants, tan shorts, blk shorts Socks: red, blue, black, tan, white How many days in a row could you come to school with a different outfit? Sample space: What are the odds of wearing black pants and red socks? Odds = 3 60โ3 = 1 19 Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts White Shirt Black Shirt Blue Shirt Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan
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Sample Space Example: Your choice of school clothes: Shirt: blue, white, black Bottoms: blk pants, tan pants, tan shorts, blk shorts Socks: red, blue, black, tan, white How many days in a row could you come to school with a different outfit? Sample space: What are the odds of wearing black pants and red socks? Odds = 3 60โ3 = 1 19 Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts Black pants Black Shorts Tan pants Tan Shorts White Shirt Black Shirt Blue Shirt Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan Blue Black white Red Tan Blue Black Red white Tan Blue Black white Red Tan What are the odds against wearing a blue shirt and white socks? Odds against (blue shirt and white socks) = 60โ4 4 = = 14 1
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Homework Worksheet 13.1
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