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- A cinema hall holds 100 people. The probability of individual transmission, that is, the probability for each individual in the cinema that they have Covid-19 and pass it to you, is 0.1. Answer the following question parts. (a) Calculate the probability that you contract Covid-19. [ Hint: start by finding the probability that you do not contract it. ] (b) The Cinema introduces a mask mandate, so that the probability of individ- ual transmission is reduced by a factor of 3. Redo your calculation that you contract the virus. (c) A new rule is introduced that everyone in the cinema must be vaccinated. This reduces the probability of individual transmission by a factor of 10. Redo your calculation that you contract the virus.Suppose that the probability that a child living in an urban area in the United States is obese is 20%. If a social worker sees 15 children living in urban areas, what is the probability that 5 are obese? Enter response as .xxxxA binary message (0 or 1) is communicated through a noisy channel with A as the message transmitted and B as the message received. Assume that A=0 and A=1 is transmitted with equal probability, and the received message is 90% correct of the time. With this, determine the joint PMF of A and B. Choose the answer for each question among the following: 0.05, 0.10, 0.40, 0.45. ii. 111. iv. P(A=1, B=0) P(A=1, B=1) P(A=0, B=1) P(A=0, B=0)
- A binary communication channel carries data as one of two types of signals denoted by 0 and 1. Owing tonoise, a transmitted 0 is sometimes received as a 1 and a transmitted 1 is sometimes received as a 0. For agiven channel, assume a probability of 0.94 that a transmitted 0 is correctly received as a 0 and a probability0.91 that a transmitted 1 is received as a 1. Further assume a probability of 0.45 of transmitting a 0. If asignal is sent, determine1. Probability that a 1 is received2. Probability that a 0 is received3. Probability that a 1 was transmitted given that a 1 was received4. Probability that a 0 was transmitted given that a 0 was received5. Probability of an errorA company prices it's tornado insurance using the following assumptions: in any calendar year there can be at most one tornado in any calendar year the probability of a tornado is 0.15 The number of tornadoes in any calendar year is independent of the number of tornadoes in any other calendar year using the companies assumptions calculate the possibilities that there are fewer than 2 tornadoes in a 20 year.Suppose in your closet you have 9 sweaters, 5 of which have buttons, and 15 shirts, 7 of which have buttons. If you randomly reach into your closet and pull out one sweater and one shirt, what is the probability that both have buttons? QUESTION 8 O 5/24 7/24 = 35/576 = 88175 112 O 5/9 +7/15 O 5124 7/24 = 7/15 6|g o 7127
- A company prices its tornado insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.13. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 25- year period. Round your answer to 4 decimals. Show your work. Show what you entered into your calculator.Suppose that ina certain small town it either rains or is sunny every day. A meteorologist notes that when it is sunny in this town, it will be sunny the next day with probability 0.6. If it rains, it will be sunny the next day with probability 0.7. Answer the following questions: 1. What is the probability that it will rain the next day if it was sunny the previous day?A student gets selected by 53% to go on a science trip. Let X = the number of students who get selected in the next 6 students we have chosen at random. what is the probability that X is at most 1 O a. 0.989221 O b. 0.022164 O c. 0.083711 O d. 0.977836
- A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.050.05. On visiting a holiday resort for seniors, he sells 1010 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 1010 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places.Part a)What is the expected number of policies that will pay out before the insured parties have reached age 61?Part b)What is the variance of the number of policies that will pay out before the insured parties have reached age 61?Part c)What is the probability that at least two policies will pay out before the insured parties have reached age 61?Suppose that a single card is selected from a standard 52-card deck. What is the probability that the card drawn is a spade? Now suppose that a single card is drawn from a standard 52-card deck, but it is told that the card is black. What is the probability that the card drawn is a spade? .... The probability that the card drawn from a standard 52-card deck is a spade is (Round to three decimal places as needed.) The probability that the card drawn from a standard 52-card deck is a spade, given that this card is black, is . (Round to three decimal places as needed.) O Time Remaining: 02:42:40 Next MacBook Pr 吕口 DOO O00 DII DD esc F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 $4 4. 6. 08. Left ER Rahi W tab S. S LO %#3If a graduate student is randomly selected, find out the probability that that particular student's birthday is NO in day in May (In calculating the probability, ignore the inclusion of leap years). a. 31/364 b. 334/365 c. 31/365 d. 11/12
