An art dealer receives a shipment of five old paint-ings from abroad, and, on the basis of past experience, she feels that the probabilities are, respectively, 0.76, 0.09,0.02, 0.01, 0.02, and 0.10 that 0, 1, 2, 3, 4, or all 5 of themare forgeries. Since the cost of authentication is fairly high, she decides to select one of the five paintings at ran-dom and send it away for authentication. If it turns out that this painting is a forgery, what probability should shenow assign to the possibility that all the other paintingsare also forgeries?

where the first outcome is one of X, Y, and Z, and the second outcome in each case is one of A and B. Use the following probabilities instead of those given in your text: Pr[X]=37 Pr[Y]=27Pr[Z]=27Pr[A|X]=45Pr[B|X]=15Pr[A|Y]=23Pr[B|Y]=13Pr[A|Z]=18Pr[B|Z]=78 Pr[(XorY)|B]=

Suppose there are exactly three states of weather: sunny, cloudy, or rainy. If it is sunny today, then the probability is 3/4 that it will be sunny tomorrow, 1/8 that it will be cloudy tomorrow, and 1/8 that it will be rainy. If it is cloudy today, then the probability is 1/2 that it will be sunny tomorrow, 1/4 that it will be cloudy tomorrow, and 1/4 that it will be rainy. If it is rainy today, then the probability is 1/4 that it will be sunny tomorrow, 1/2 that it will be cloudy tomorrow, and 1/4 that it will be rainy. cloudy is From this Markov model, for any given day the probability that it will be sunny is rainy is Round your answers to three decimal places. and

If the student attends class on a certain Friday, then he is five times as likely to be absent the next Friday as to attend. If the student is absent on a certain Friday, then he is three times as likely to attend class the next Friday as to be absent again.