One of two biased coins A and B is selected and flipped 3 times. Let A be the event that coin A is selected and B be the event that coin B is selected, with probabilities p(A) = 0.4 and p(B) = 0.6. When coin A is flipped, the probability of heads is 0.2. When coin B is flipped, the probability of heads is 0.8. Let HHH be the event that the selected coin comes up heads 3 times. Complete the values X, Y, and Z in Bayes' Theorem to determine the probability coin B was chosen if all 3 flips come up heads. X Ex: 0.123-0.6 p(B|HHH) = Ex: 0.123 Y 0.6+Ex: 0.123 Ꮓ . 0.4
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- A distribution of values is normal with a mean of 211 and a standard deviation of 50.4. Find the probability that a randomly selected value is between 59.8 and 155.6. P(59.8 X 155.6) = Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z - scores rounded to 3 decimal places are accepted.If the probability of an event is 62%, what is the probability of its complement?This exercise asks you to (partly) verify that linearity of expectation holds even if the random variables are not independent. Consider two 6-sided dice that are rolled independently. What is the expected value of the sum? Now consider the case where the first die is rolled normally and then the second die is set equal to the value shown on the first die. What is the expected value of the sum? Now consider the case where the first die is rolled normally and the second die is set equal to 7 minus the value of the first die. What is the expected value of the sum?
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- A fair coin is flipped 12 times in a row. a What is the probability that it lands on tails exactly one third of the times? b What is the probability that it lands on heads at least twice? c What is the probability that the first flip is heads or the last flip is heads?A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 13 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 54 bolts. The sample mean bolt length was 13.05 centimeters. The population standard deviation is known to be o = 0.18 centimeters. What is the test statistic z? Ex: 1.23 What is the p-value? Ex. 0.123 Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of a = 0.01? SelectThree coins are tossed at the same time, each equally likely to come up heads or tails. What is the probability of getting 1 head and 2 tails?
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