Write I if the event is independent. Otherwise, write D
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- a) In a pastry shop in a small town, the probability that a customer buys apple tarts is 0.45, the probability they buy an apple pie is 0.69 and the probability that they buy both an apple tart and an apple pie is 0.27. A customer is chosen at random. i. Find the probability that they buy an apple tart or an apple pie. ii. Given that a customer buys an apple pie, what is the probability that they also buy an apple tart?Your company bids for two contracts. You believe the probability that you get contract #1 is 0.7. If you get contract #1, the probability you also get contract #2 will be 0.3, and if you do not get contract #1, the probability that you get contract #2 will be 0.2. Complete parts a through e below. Question content area bottom Part 1 a) Are the outcomes of the two contracts bids independent? Explain. b) Find the probability you get both contracts. c) Find the probability you get neither contracts. d) Let X be the number of contracts you get. Find the probability model for X. x 0 1 2 P(x) e) Find the expected value and standard deviation of X.d) Suppose we want to pick two numbers from {1,2, ..,100} randomly. What is the probability that the sum of the two picked numbers is divisible by 5.
- A school has 200 students with 80 students taking each of the three subjects trig, probability, and basket-weaving. There are 30 students taking any given pair of these subjects, and 15 students taking all three subjects. A) How many students are taking non of these three subjects? B) How many students are taking only probability?1 R 3.) Suppose that a single card is selected from a standard 52-card deck. a.) Compute the probability of the event E = "drawing a king." b.) Compute the probability of the event E = "drawing a king" or F = "drawing a queen" or G = "drawing a jack." c.) Compute the probability of the event E= "drawing a king" or F = "drawing a diamond." Q Search olo 15 10 5 T G f6 4- 6 Y H f7 & ♫+ 7 lıyı C f8 * 00 fg I 9 J K 0 O + f10 DII L E 200m DDI a 112 C ** 86.) A mathematics class has 16 engineers majors, 12 science majors, and 4 liberal artsmajors.a.) What is the probability that a student selected at random will be a science orliberal arts major?b.) What is the probability that a student selected at random will be anengineering or science major?c.) 5 of the engineering students, 6 or the science majors, and 2 of the liberal artsmajors are female. What is the probability that a student selected at random is anengineering major or a female?
- Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.2.3 4) Consider each situation. Decide whether the pairs of events are mutually exclusive or not. a) Roll a die: Get an even number and get a number less than 3. b) Roll a die: Get a prime number (2, 3, or 5) and get a six. c) Roll a die: Get a number greater than 3 and get a number less than 3. d) Select a student: Get a student with blue eyes and get a student with blond hair. e) Select a college student: Get a sophomore and get a student that is a math major. f) Select a course: Get an Algebra course and get an English course. g) Select a voter: Get a Republican and get a Democrat. INTL DII %23 3. 4 5 6. e y3.) A card is selected from an ordinary deck of 52 cards. What is the probability of getting (Example 2 on page 158) (show your work) A.) a face card that is a club B.) an ace and a queen C.) a jack or a spade