m #4: A man and woman agree to meet at a certain location at 12:36 pm. If the man arrives at a time that is uniformlydistributed between 12:25 pm and 12:48 pm, and if the woman arrives independently at a time that is uniformlydistributed between 12:00noon and 1:00 pm, what is the probability that the man arrives first?roblem #4:Enter your answer symbolically,as in these examples

Answered: Image /qna-images/answer/b6e0a8c5-37c8-4266-a1d2-d396c1bc46ef.jpg

Answered: 4: A man and woman agree to meet at a…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.2: Probability

Problem 39E: Spinner A and B shown in the figure are spun at the same time. (a) Are the events "spinner A stops...

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Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month, a Brand A user has a 20 probability of switching to Brand B and a 5 of not using either brand. A Brand B user has a 15 probability of switching to Brand A and a 10 probability of not using either brand. A nonuser has a 10 probability of purchasing Brand A and a 15 probability of purchasing Brand B. How many people will be in each group a in 1 month, b in 2 months, and c in 18 months?
Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one pack or less per day. During any month, there is a 5 probability that a nonsmoker will begin smoking a pack or less per day, and a 2 probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10 probability of quitting and a 10 probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 5 probability of quitting and a 10 probability of dropping to a pack or less per day. How many people will be in each group a in 1 month, b in 2 months, and c in 1 year?
If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the expected value of this game is E=0.9+0.1= .
Lana arrives at a bus stop at a uniformly random time. When Lana arrives at the bus stop, either of two independent bus lines (both of which can take her school) may come by. Company A’s bus arrival times are exactly 10 minutes apart, whereas the time from one Company B bus to the next is distributed as Expo (1/10) . What is the probability that Company B’s bus arrives first solve by double integration.
In a lake, Peter catches fishes in an average rate of 3 fishes per hour. (Assume Peter alwayscatches one fish at a time and the events of catching each fish are independent.)(a) At 2:00PM, if it’s known that Peter caught the previous fish at 1:50PM, what is the probability that he will catch the next fish before 2:30PM?(b)Assume Peter starts catching fish at 9:00AM, what is the probability that he will catch the 2nd fish between 9:30 and 9:50AM?
A Sugar Processing Plant operates its four evaporators A, B, C, and D at 40%, 30%, 20%, and 30% of the time, respectively. The chemical engineer always speeds to work, and he has the probability 0.2, 0.1, 0.5, and 0.2 of attaining those operating schedules. What is the probability that he’ll not be able to operate as scheduled for five consecutive days?a) 0.27 b) 0.09 c) 0.18 d) 0.36 e) None of these
1. In 1881, Simon Newcomb discovered that digits do not occur with equal frequency. After studying lots of data, he assigned probabilities for each of the first digits of numbers. This is known as Benford’s Law (because a physicist named Frank Benford proved it at a later date) and plays a major role in identifying tax fraud. Digit Probability1 0.3012 0.1763 0.1254 0.0975 0.0796 0.0677 0.0588 0.0519 0.046 A.) Verify that this is a probability model.B.) Use Benford’s Law to determine the probability that a randomly selected first digit is 1 or 2.C.) Use Benford’s Law to determine the probability that a randomly selected first digit is at least 6.2. 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…
c. A jet fighter consists of two engines. The probability that the second engine functions in a satisfactory manner during its design life is 0.96, and the probability that at least one if the two engines does so is 0.98 and the probability that both engine do so is 0.935. Given that the first engine functions in a satisfactory manner throughout its design life, what is the probability that the second one also?
6 - If the random variable X has a Poisson distribution with parameter 9, which of the following is the probability of P(X<14) using the central limit theorem? a) 0.6826 B) 0.8413 NS) 0.9332 D) 0.1826 TO) 0.0336
3a) A discrete random variable X has a probability function as shown in the table below, where a and b are constants. x 5 10 15 20 P(X=x) a 0.1 b 0.35 Given that E(X) = 13.75 Find the value of a and the value of b. 3b) Please write down your answer as a decimal number with 2 decimal places. Using the formula and previous answers find Var(X) 3c) Using the formula and previous answers find E( 6 – 8X ) 3d) Using the formula and previous answers find Var( 6 – 8X )
In a certain factory, machines I, II, and III are all producing springs of the same length. Machines I, II, and III produce 1%, 4%, and 2% defective springs, respectively. Of the total production of springs in the factory, Machine I produces 30%, Machine II produces 25%, and Machine III produces 45%. If one spring is selected at random from the total springs produced in a given day, determine the probability that it is defective.?
Example 4-18. At Least One Paid Assistantships Of Ph.D. students, 60% have paid assistantships. If 3 students are selected at random, find the probability that at least 1 has a paid assistantship. Solution:

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