If a person watches a certain TV daily evening news program on one evening, then theprobability that the person watches that program the next evening is 0.7. However, if the persondoes not watch the program one evening, then the probability that the person watches theprogram the next evening is 0.2.a) If the person watches the program on Monday, what is the probability that the personwatches the program on Wednesday?b) If 20% of the population watches the program on Thursday, what percentage can beexpected to watch on Friday?c) What is the steady-state probability of watching?Note: leave your answer as a percentage, rounded to 2 decimal places
Question
If a person watches a certain TV daily evening news program on one evening, then theprobability that the person watches that program the next evening is 0.7. However, if the persondoes not watch the program one evening, then the probability that the person watches theprogram the next evening is 0.2.a) If the person watches the program on Monday, what is the probability that the personwatches the program on Wednesday?b) If 20% of the population watches the program on Thursday, what percentage can beexpected to watch on Friday?c) What is the steady-state probability of watching?Note: leave your answer as a percentage, rounded to 2 decimal places
Solution
a) The probability that the person watches the program on Wednesday given that they watched it on Monday can be calculated by multiplying the probability that they watch it on Tuesday (given that they watched it on Monday) by the probability that they watch it on Wednesday (given that they watched it on Tuesday). Since both of these probabilities are 0.7 (according to the problem), the calculation is 0.7 * 0.7 = 0.49. So, there is a 49% chance that the person will watch the program on Wednesday if they watched it on Monday.
b) If 20% of the population watches the program on Thursday, then the probability that they watch it on Friday is 0.2 (according to the problem). So, 20% * 0.2 = 4%. Therefore, we can expect 4% of the population to watch the program on Friday.
c) The steady-state probability of watching can be found by setting up and solving the following equation: P = 0.7P + 0.2(1-P), where P is the steady-state probability. Solving for P gives P = 0.2 / (1 - 0.7) = 0.2 / 0.3 = 2/3 = 0.6667. So, the steady-state probability of watching is approximately 66.67%.
Similar Questions
A survey showed that 25% of college students read newspapers on a regular basis and that 81% of college students regularly watch the news on TV. The survey also showed that 21% of college students both follow TV news regularly and read newspapers regularly.Answer the questions below. (If necessary, consult a list of formulas.)(a) What is the probability that a student watches TV news regularly, given that he or she regularly reads newspapers? Round your answer to 2 decimal places.(b) What is the probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly? Round your answer to 2 decimal places.
Students in a school were surveyed about their study habits. Forty-two percent of students said they study on weeknights and weekends, 47% said they studied on weekends, and 65% said they study either on weeknights or weekends. If you were to pick one student at random, what is the probability that he or she studies on a weeknight?40%60%45%50%
1 pointA person predicts daily whether the price of stocks of wrist watch companies will go up or down. If his prediction on stock price of Titan is correct 2 times out of 4, for Rolex it is correct 6 times out of 8 and for Fossil it is correct 5 times out of 9, then what is the probability that at least two of his predictions are correct on a given day?
In a survey conducted in a neighbourhood, it was found that 25% of the residents watch movies in theaters, 35% watch movies on streaming platforms, and 15% watch movies through both theaters and streaming platforms.What is the probability that a randomly selected resident does not watch movies either in theaters or on streaming platforms?
Everyday, Rohan learns either football or cricket. If he play football one day, he has a 0.6 probability of playing cricket in the following day. If he play cricket one day, he has a probability of 0.4 on playing football the next day. What is the probability that Rohan will play football on Wednesday given that he play football on Monday? 0.24 0.36 0.4 0.6
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.