Find the number of outcomes of the sample space of each event • Throwing a fair dice • Drawing a card from a standard deck of cards • Tossing a coin and two dice • Tossing a dice and a coin
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Q: 2. Tossing 2 dice, a) What is the sample space? b) Draw the histogram. c) Find the probability of…
A: Two dice are rolled, => we will have 6*6 = 36 outcomes in sample space
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- A sample space contains number of pins of a 12-pin IC that are not functioning. Event ‘unacceptable’ takes place when more than or equal to half the pins are not functioning. Event ‘acceptable’ takes place when more than 10 pins are functioning. (note: write down the accurate sample space for the experiment first. Check again if the outcomes in sample space represent all possibilities of observations for this experiment) Identify outcomes contained in each event. Identify if the two events are independent.Consider the sample space S (Algebra, Trigonometry, Calculus, Chemistry, Physics, Biology, Filipino} A = [ Algebra, Trigonometry, Filipino} B = (Trigonometry, Calculus, Chemistry) %3D C= (Biology) %3D List the element(s) of the sets corresponding to the event: (An B') UC O LANB)UC =[Algebra, Filipino} O LANB)UC =(Algebra, Trigonometry, Filipino ) O (An B') UC =(Algebra, Biology, Physics, Filipino} O An B)uC= ( Algebra, Trigonometry, Calculus, Chemistry, Physics, Filipino ) %3DA sample space contains seven simple events: E,, E,, ..., E,. Use the following three events-A, B, and C. B = {E, E, E, E;} c={E, E;} A = 4' List the simple events in the following. (Enter your answers as a comma-separated list.) not A
- Given the following sample space and event: S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {even number} What is P(A)?7) Four students will be randomly selected from the six top students in mathematics to represent their school in a regional competition. Angela and Brian are among the six students, and they wish to determine the probability that they will both be chosen. Describe (list) the sample space for determining this probability. What is the probability they will both be chosen?The sales of a coffee shop in a commercial district is very difficult to predict. The total revenue of the shop can be very good one day and bad the other day. The revenue can be classified into three different categories as High, Medium or Low a) Explain how we can see the revenue of the coffee shop as a "Random Experiment" b) Write down the sample space of this random experiment. c) Write down the event that revenue is high or medium using set notation. Write down a new event that is disjoint (mutually excusive) to the previous event. d) What would be the appropriate observation points (epochs) of the revenue? Explain.
- An experiment consists of randomly obtaiming five numbers without replacement from the equiprobable sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Find, with clear explanation, the probability that each number chosen is larger than the previous one.last school year the student body of local univ. consisted of 24 percent of freshman 20 percent sophmore 32 percent junior and 18 percent seniors. A sample of 400 students taken from this year's student body showed the following number of students in each class freshman 113 sophmores 98 juniors 115 seniors 74 is there a significant change in the classifications between the last school year and this school year what is the expected number of sophmores? 104 128 98 72 96Five state officials are listed to the right. Lieutenant Governor (L) Secretary of State (S) Attorney General (A) Representative (R) Press Secretary (P) a. List the 10 possible samples (without replacement) of size 3 that can be obtained from the population of five officials. b. If a simple random sampling procedure is used to obtain a sample of three officials, what are the chances that it is the first sample on your list in part (a)? the second sample? the tenth sample? a. List all 10 possible samples (without replacement) of size 3. Use the letter abbreviation for each official. (Use a comma to separate answers as needed.) b. What is the chance that the first sample in your list is selected? Type an exact answer.) What is the chance that the second sample in your list is selected? Type an exact answer.) What is the chance that the tenth sample in your list is selected? (1)
- a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product.If a person rolls a six-sided die and then draws a playing card and checks its color, describe the sample space of possible outcomes using 1, 2, 3, 4, 5, 6 for the die outcomes and B, R for the card outcomes. S = { } A survey of 500 randomly selected high school students determined that 480 play organized sports. What is the probability that a randomly selected high school student plays organized sports? P(plays organized sports) =