1. U = {1, 2, 3, 4, 5, … 10} A = {6,7,8,9,10} B = {1, 3, 5, 7, 9}, C = { 2, 4, 6, 8, 10} b) Find B’ c) Find A ∪ (B ∩ C)
2. Use Venn diagrams to show why A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).
3. In a large class, there are 45 students who are either on a sports team or involved in an academic club (such as Forensics team). There are 22 students on a sports team and 27 students in an academic club. How many are both on a sports team and an academic club.
4. A city offers three types of mass transit: buses, subways, and trains. A survey of 200 city residents found the following 73 did not use any mass transit at all 82 used the subway 44 used only the subway 28 used both the bus and the subway 59 used the train. 10 people used all three types of transit 15 people used both the train and the bus. Draw a Venn diagram with circles for B (bus), S (subway) and T(train). Fill in the numbers. How many people in the survey used only the train? How many used only one type of mass transit (only bus or only train or only subway)?
since the number of person who use any one of the transits are 200-73=127
And 33 people use more than one transit.
Thus of the number of people use only one type of mass transit are 94
i am sure that 2 and 3 are true but not sure if 1 is true QUESTION 6 Durian is a fruit that is particularly popular in Singapore and Malaysia. Durian has a very strong smell, which many people dislike. As a result, the Singapore Mass Transit Authority bans people from carrying durians on Singapore's trains. 1. Transporting durians on the train has economic implications for passengers. 2. If the Singaporean Mass Transit Authority did not intervene then it is...
Problem 1: Suppose we survey 500 students about their opinions on different sports leagues. We find that 215 students like the NFL, 305 students like the NBA, and 170 students like both the NFL and the NBA. a. Complete the Venn Diagram: b. How many students don’t like either the NFL or the NBA? c. What is the probability that a student likes only the NBA?
1. Let A be the set whose elements are the months of the year that begin with the letter J. A = { } 2. Define a set that is empty. Let B be the set: _________________________________________________________________________ _________________________________________________________________________ 3. The following data was collected from a survey of 350 San Antonio residents Are you a Spurs fan? YES NO Male 204 19 Female 113 14 a. How many males were surveyed? b. How many spurs fans were surveyed? c. How...
(10 points) 6. At Wassamata U, Bullwinkle did a survey of 150 of his fellow graduates. He found that 64 had taken a math class. 53 a chemistry class, and 60 a physics class. He also found 23 took both math and chemistry, 24 took chemistry and physics, 29 took math and physics while 10 took all 3 of the subjects. Complete the Venn diagram a) Wassamatta U Chemistry Math Physics How many students took only two of the three...
Counting 1. Our student clubs are being particularly active. The aquatics club in particular is in training for an upcoming competition. For all parts of this question, working is required, including combinatoric/factorial notation as needed as well as final answers. a) 12 12 5 marks] During training, there are several different types of laps that can be swum: freestyle arms only freestyle one arm only, left then right torpedo/kickboard (straight kicking legs only) backstroke breaststroke Assume that each type is...
please answer part e) only. i have already dealt with a,b,c,d. Exercise 5. Transportation for Away Games (Perfect Substitutes) Your college football team is playing an away game against their division rival. As president of the fan club your utility is represented by the maximum number of fans you can transport to the game. You have to choose between vans (xi) that hold 10 students, drbuses (x2) that hold 50 students. You determine that your utility function is u=10x1 +...
8-10 0.4, P(B)0.5, and P(A UB)-0.7, find P(An B) P(A' U B') 6. If P(A) a. b. 7. A coin is tossed 4 times and the sequence of heads and tails is observed a. b. What is the sample space S for this experiment? Consider the following events: A [at least 3 heads) B- (at most 2 heads) C- (heads on the 3rd toss) D - [1 head and 3 tails) If the outcomes in S are equally likely, find...
Help 8-10 0.4, P(B)0.5, and P(A UB)-0.7, find P(An B) P(A' U B') 6. If P(A) a. b. 7. A coin is tossed 4 times and the sequence of heads and tails is observed a. b. What is the sample space S for this experiment? Consider the following events: A [at least 3 heads) B- (at most 2 heads) C- (heads on the 3rd toss) D - [1 head and 3 tails) If the outcomes in S are equally likely,...
7-10 help 0.4, P(B)0.5, and P(A UB)-0.7, find P(An B) P(A' U B') 6. If P(A) a. b. 7. A coin is tossed 4 times and the sequence of heads and tails is observed a. b. What is the sample space S for this experiment? Consider the following events: A [at least 3 heads) B- (at most 2 heads) C- (heads on the 3rd toss) D - [1 head and 3 tails) If the outcomes in S are equally likely,...
Put the following sampling situations in the order 1. Cluster 2. Systematic 3. Stratified 4. Simple Random options: A) As the people entered the airport every 8th person was sniffed by the police dog. B) From a large college campus everyone taking a statistics course is selected to complete a survey. C) From each grocery store in the city a the price of three random cans of soup is collected. D) By using current student numbers a select group of...