1) IfX~B(10,0.7), find the probability for P(X=5)
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- Find the probability that the sum of two dice will be less than 7, given that the first dice is a 5.Let A = “ sum of toss of two dice is < 7.” B = “first dice tossed was a 5”.You and your best friend are part of a group of 102 students which are to be divided into 3 classes of equal size. The probability that you and your best friend end up in the same class is defined to be the ratio T/A, where: T-number of ways you and your best friend end up together in the same class, and • A-number of ways to divide 102 students into 3 groups of equal size. What is the probability that you and your friend will end up in the same class? (Note: every probability is a number between 0 and 1 which represents the likelihood of a particular outcome; the closer the probability is to 1, the more likely the outcome.) (Enter your answer as a decimal rounded to 4 decimal places.) .Choose the correct option
- Gregory buys a bag of cookies that contains 7 chocolate chip cookies, 5 peanut butter cookies, 8 sugar cookies and 8 oatmeal cookies. What is the probability that Gregory reaches in the bag and randomly selects an oatmeal cookie from the bag, eats it, then reaches back in the bag and randomly selects a peanut butter cookie? Give your answer as a fraction, or accurate to at least 4 decimal places.A coin is in one of 5 boxes. The probability that it is in the ith box is (i/15). If you search in the ith box and it is there, you find it with probability (4/5). Find the probability that the coin is in the 3rd box given that you have looked in the 1st box and did not find it.If X N(5,4), then what is the probability that 8 < Y < 13 where Y = 2r +1?
- Q 2. (a) The probability that a student passes the P&S exam is 0.7. (1) Find the probability that a given student will pass the P&S exam after the third try. (ii)Find the probability that the third student who fails the P&S exam is found after the fifth student in a class of 9 students? (ii)Find the probability that at most 3 students will pass the P&S examina class of 7 students. 6Find the probability a randomly selected z-score is less than -2.1. Round your result to 4 decimal places.Fiona walks from her house to a bus stop where she gets a bus to school. Hertime, W minutes, to walk to the bus stop is normally distributed with W-N (12^3) Fiona always leaves her house at 07:15. The first bus that she can get departs at 07:30. a) Find the probability that it will take Fiona between minutes andminutes to walk to the bus stop. The length of time, minutes, of the bus journey to Fiona’s school is normallydistributed with B-N (50, σ^2) . The probability that the bus journey takes less than60 minutes is 0.941. b) Find σ c) Find the probability that the bus journey takes less than 45 minutes. If Fiona misses the first bus, there is a second bus which departs at 07:45. Shemust arrive at school by 08:30 to be on time. Fiona will not arrive on time if shemisses both buses. The variables W and B are independent. d) Find the probability that Fiona will arrive on time This year, Fiona will go to school on 183 days.e) Calculate the number of days Fiona is expected to arrive…
