Probability Assignment: Understanding Key Concepts in STAT 2040

STAT 2040 Section 2 – Probability Assignment Then save and when completed, upload to the correct place. Problem 1 Which of the following values cannot be probabilities? -2, 0, 1, 2, .0123, 4/5, 7/3, 0.9999 -2,2,7/3' because probalities have to be greater than 0 less than 1 2 What is the probability of an event that is absolutely certain to happen? What is the probability Probability of certain event= 1 Probability of impossible event= 0 3 0.375 4 Probability= 0.0625 5 Once you start working on this assignment, please change the file name to " Assignment 2_Firs There are 8 possible boy/girl outcomes when 3 children are randomly selected (2x2x2=8). Find t selected children there is exactly 1 girl. Probabilit y= Among 80 women who are pregnant, a pregnancy test yielded the wrong results 5 times. Based for a woman who is pregnant? Is it "unusual" for a pregnant woman to get a wrong test result? ( is less than or equal to 0.05) its probability is not unusual because the probability is over 0.05 A study of 150 randomly selected American Airlines flights showed that 110 arrived on-time. Wh arriving late? Is it "unusual" for an American Airlines flight to arrive late?

Probability= 40 0.266666666666667 6 Probability= 0.682 7 Identify the correct description of the complement of the following event. When several textbooks are returned from editing, none of the books are found to have any err At least one of the texbooks is errorless 8 Identify the correct description of the complement of the following event. When 100 engines are shipped, all of them are free of defects. At least one of the engines is defective 9 Express the following as a probability value. "It will definitely turn dark tonight." 1 10 12 0.7511111111 78 SUM= 90 not unusual because the probability is over 0.05 When a woman over the age of 25 is randomly selected, there is a 0.318 probability that she has randomly selected, find the probability that she does not have a bachelor's degree. A batch consists of 12 defective coils and 78 good ones. Find the probability of getting two good selection is replaced before the second is made. (hint: this is probability of good AND good) Defective coils= P(good *2nd good selection)= Good coils=

11 74613 1/74,613 12 0.0322580645161 13 336 14 smoker= 43 total people= 176 smoker= 30 total people= 134 smoker= 28 total people= 86 A state lottery involves the random selection of six different numbers between 1 and 22. If you s probability that it will be the winning combination? In this problem the ordering of the numbers problem not a permutation problem). Assume that one student in your class of 31 students is randomly selected to win a prize. Would to be "unusual" if its probability is less than or equal to 0.05) Yes, it would be unusual because it is less than 0.05 There are 8 members on a board of directors. If they must elect a chairperson, a secretary, and a possible? (hint: order matters in this case) A study of consumer smoking habits includes 176 people in the 18-22 age bracket (43 of whom s smoke), and 86 people in the 31-40 age bracket (28 of whom smoke). If one person is randomly someone who is age 18-22 OR does not smoke. 18-22 age bracket people who don’t smoke= 23-30 age bracket people of age 18-22 non- smoking= 31-40 age bracket P(18-22 or does not smoke)=

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15 177 43 0.42156862745098 134 30 86 29 397 102 16 0.25 or 1/4 17 Express the indicated degree of likelihood as a probability value. "There is a 40% chance of rain t 0.40 18 A study of consumer smoking habits includes 177 people in the 18-22 age bracket (43 of whom s smoke), and 86 people in the 31-40 age bracket (29 of whom smoke). If one person is randomly someone who is age 18-22 GIVEN that they smoke. 18-22 age bracket= 23-30 age bracket= 31-40 age braacket= On a multiple choice test with four possible answers for each question, what is the probability o guess? 100 employees of a company are asked how they get to work and whether they work full time o the 100 employees is randomly selected, find the probability of getting someone who carpools, part time. 1. Public transportation: 10 full time, 6 part time 2. Bicycle: 3 full time, 4 part time 3. D time, 7 part time

0.6607 bicycle drive alone carpool total 19 17 wrestlers compete in a competition. If each wrestler wrestles one match with each other wre 136 20 6 0.5 6 12 21 public transportation P(carpool,cycl e,or part time)= A study examined the number of cylinders (4, 6, and 8) and the type of transmission (manual or is the data collected. Nine of the cars had 4 cylinder engines and 6 of these had automatic trans had automatic transmissions. Five cars had 8-cylinder engines and 4 of these had automatic tran selected that it has a manual transmission or has a 6-cylinder engine. Manual transmissi on total= P(Manual or 6 cylinder)= 6 cylinder engine total= A study examined the number of cylinders (4, 6, and 8) and the type of transmission (manual or is the data collected. Nine of the cars had 4 cylinder engines and 6 of these had automatic trans had automatic transmissions. Five cars had 8-cylinder engines and 4 of these had automatic tran selected that it has a manual transmission and an 8-cylinder engine.

6 0.05 5 22 270725 1/270,725 or 0.000004 23 If a couple plans to have 6 children, what is the probability that they will have at least one girl? P(at least 1 girl)= 63/64 0.984375 P(all boys)+P(not all b 1 P(not all boys)= 1-P(all boys) 24 126 792 0.1590909090909 Manual transmissi on total= P(manual transmission and 8-cylinder engine)= 8 cylinder engine total= From a deck of playing cards, find the probability of randomly selecting all four aces as the first f replaced. A carton contains 12 eggs, 3 of which are cracked. If we randomly select 5 of the eggs, what is th Assume there is no replacement. # of ways to pick 2 # of ways to pick 5 of 12= Prob(5 not cracked)=

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25 # of ways to pick 2 cracke 3 # of ways to pick 3 not cracked= 84 # of ways to pick 5 of 12= 792 Prob(2 cracked of 5 picked)= A carton contains 12 eggs, 3 of which are cracked. If we randomly select 5 of the eggs, what is th cracked? Assume that no eggs are replaced.

Name: Xia Jones of an impossible event? stName_LastName.xlsx " the probability that among 3 randomly on this data, what is the probability of a wrong test result (hint: consider the event to be "unusual" if its probability hat is the probability on an American Airlines flight

rors. s a bachelor's degree. If a woman over the age of 25 is d coils when two coils are randomly selected if the first

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295 133 0.853535354 select one six number combination, what is the s does not matter (hint: that means it is a combination d it be "unusual" for you to win? (hint: consider the event a treasurer, how many different slates of candidates are smoke), 134 people in the 23-30 age bracket (30 of whom selected from this sample, find the probability of getting

tomorrow." full time part time total smoke), 134 people in the 23-30 age bracket (30 of whom selected from this sample, find the probability of getting of answering a question correctly if you make a random or part time. The data below shows the results. If one of someone who cycles to work, OR someone who works Drive alone: 28 full time, 32 part time 4. Carpool: 10 full

10 6 16 3 4 7 28 32 60 10 7 17 51 49 100 estler, what are the total numbers of matches? automatic) among 20 randomly selected cars. Following smissions. Six cars had 6-cylinder engines and 4 of these nsmissions. Find the probability that if one car is randomly automatic) among 20 randomly selected cars. Following smissions. Six cars had 6-cylinder engines and 4 of these nsmissions. Find the probability that if one car is randomly

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four cards you select. Assume that none of the cards are he probability that none of the selected eggs are cracked?

0.318181818 he probability that exactly two of the selected eggs are

Assignment 2_Xia_Jones-2

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