Question 1 1 pts Consider the sample space and two events A and B as is illustrated in the following figure. Suppose that P({E1}) = .05, P({E2]) = .15, P({E3]) = .25, P({E4}) = .1, P({E5]) = .05, P({E6}) = .15, P({E7}) = .25. Determine P(AC U BC ). B O E1 OE 2 O E4 o E5 O E3 O E7 . E6 S S = {E1, E2, E3, E4, E5, E6, E7} is the sample space. A = {E1, E2, E3, E5, E6} B = {E2, E3, E4, E7} O .25 0 0.4 0 1 Oo 0 . 6 O .75Question 2 1 pts Three fair coins are ipped. What is the probability that we observe exactly two tails? (Suppose the sample space of this experiment consists of equally likely basic outcomes.) 0 6/8 0 1/8 C) 4/8 0 3/8 Question 3 1 pts In a telephone survey of 1000 adults, respondents were asked about the expense of a college education and the relative necessity of some form of nancial assistance. The respondents were classied according to whether they currently had a child in college and whether they thought the loan burden for most college students is too high, the right amount or too little. The proportions responding in each category are shown in the probability table below. Suppose one respondent is chosen at random from this group. What is the probability that the respondent does not have a child in college or thinks that the loan burden is a right amount? Too high Right Amount Too Little Child in College .35 .08 .01 No Child in college .25 .20 .11 O .84 O 0.2 O .64 O .44 O .69 Question 4 1 pts In a telephone survey of 1000 adults, respondents were asked about the expense of a college education and the relative necessity of some form of nancial assistance. The respondents were classied according to whether they currently had a child in college and whether they thought the loan burden for most college students is too high, the right amount or too little. The proportions responding in each category are shown in the probability table below. Suppose one respondent is chosen at random from this group. What is the probability that the respondent does not have a child in college? Too high Right Amount Too Little Child in College .35 .08 .01 No Child in college .25 .20 .11 O 0 O .56 O .44 01 Question 5 1 pts Of all those people who enter Uncle's Stereo, a discount electronics store in New York City, 25% purchase a digital camera, 6% buy a home theater receiver, and 4% buy both. Suppose a customer is selected at random. What is the probability that the customer buys either a digital camera or a home theater receiver? 0 .29 O .21 O .04 O .27 Q .31 _J l. l, ,J Question 6 1 pts Of all those people who enter Uncle's Stereo, a discount electronics store in New York City, 25% purchase a digital camera, 6% buy a home theater receiver, and 4% buy both. Suppose a customer is selected at random. What is the probability that the customer buys digital camera but not a home theater receiver? 0 .19 O .24 O .02 O .04 O .21 Question 7 1 pts Of all those people who enter Uncle's Stereo, a discount electronics store in New York City, 25% purchase a digital camera, 6% buy a home theater receiver, and 4% buy both. Suppose a customer is selected at random. What is the probability that the customer buys neither a digital camera nor a home theater receiver? 0 0.71 O 0.96 o 0.31 O 0.73 O 0.69 O 0.27 Question 8 1 pts Of all those people who enter Uncle's Stereo, a discount electronics store in New York City, 25% purchase a digital camera, 6% buy a home theater receiver, and 4% buy both. Suppose a customer is selected at random. What is the probability that the customer does not buys a digital camera? 0 0.96 o 0.94 o 0.73 O 0.75 o 0.69 Question 9 1 pts During the inaugural season of Major League Soccer in the United States, the medical teams documented 256 injuries that caused a loss of participation time to the player. The results of this investigation is shown in the following table Severity Practice(P} Game(G) Total Total 101 155 256 If one individual is drawn at random from this group of 256 soccer players, nd P(G|B). 0 44/67 0 155/255 0 44/155 0 44/256 ,l ,l L Question 10 1 pts Consider the experiment dened by the following Venn diagram such that P(E1) = .05, P(E2) = .15, P(E3) = .25, P(E4] = .40, P(E5) = .15. Let A = [E1, E2, E3} and B={E2, E3, E5}, determine P(A|B). S = {E1, E2, E3, E4, E5] is the sample space. 0 40/55 0 35/50 0 45/55 0 40/45 Question 11 1 pts For a particular disease, the probability of having the disease in a particular population is 0.05. If someone from the population has the disease, the probability they test positive of this disease is 0.92. If this person does not have the disease, the probability they test positive is 0.02. What is the probability of a random person selected from the population has a positive test result? 0 0.047 O 0.977 O 0.95 O 0.113 O 0.065 Question 12 1 pts A box contains one red, three blue, and two green marbles. Two marbles are selected at random in succession and without replacement. Let A = {at least one of the marbles is blue.] B={Both marbles selected are the same color.} Find PlAIB). O 1/4 0 4/5 0 3/4 0 1/5 Question 13 1 pts For a particular disease, the probability of having the disease in a particular population is 0.05. If someone from the population has the disease, the probability they test positive of this disease is 0.92. If this person does not have the disease, the probability they test positive is 0.02. What is the probability of a random person selected from the population is infected given that his/her test result is positive? 0 0.065 O 0.046 0 0.7077 0 0.92 Question 14 1 pts Cyber Monday is a huge online shopping day. In 2017, approximately 25% of Cyber Monday shoppers used their mobile device to make a purchase. If a person used a mobile device to make a purchase, the probability of making a purchase from Amazon was .75. Suppose a Cyber Monday purchase is selected at random. What is the probability that the purchase was made with a mobile device and was from Amazon. 0 0.5 O .3333 OI 0 0.1875 Question 15 1 pts According to a study, the percentage of households with vehicles in Boston, Massachusetts, is 66.2%; in Cambridge, Massachusetts, 73.2%; and in Worceter, Massachusetts, 80.7%. Suppose owning a vehicle in these three cities are independent of each other. If a household from each city is randomly selected, What is the probability that none of the three households has a vehicle. 0 .3376 0 0.3911 0 0.240 0 0.0174