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.

7. A drawer contains 6 black socks, 4 brown socks, and 2 green socks. Suppose one sock is drawn from the drawer and that it is equally likely that any one of the socks is drawn. Find the probabilities for each of the following: a. The sock is brown b. The sock is either black or green c. The sock is red d. The sock is not black

In a certain university the probability of randomly selecting a student that studies mathematics is 0.6 while the probability of randomly selecting a student studying literature is 0.45. Which of the following statements CAN NEVER BE TRUE? I. The probability of selecting a student studying mathematics given that he studies literature is 0. II. The probability of selecting a student that studies both science and mathematics is 0.27. O Both Statements I and Il. O StatementI only. O Neither Statement I not I. O Statement II only.

2 dice, one green and one black, are rolled once. Which of the following events are independent?A. E = A 2 is rolled on the green die, F = A sum of 8 is rolled on both dice.B. E = A sum of 3 is rolled on both dice, F = A 4 is rolled on the black die.C. E = A 2 is rolled on the green die, F = A sum of 7 is rolled on both dice.D. E = A 3 is rolled on the green die, F = A 5 is rolled on the black die.

Tara is registering for a physics class.  The morning classes are 1st, 2nd, and 3rd periods, and the afternoon classes are 4th, 5th, and 6th periods.   Below is a table of teachers and the periods they teach the math class.  If Tara requests an afternoon class, what is the probability that she will be assigned Mrs. David for 5th period?   1st 2nd 3rd   4th 5th 6th Williams X X X     X   Brown     X   X   X Davis   X X     X X Miller X X     X X

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