Conditional Probability

Andrea is a very good student. The probability that she studies and passes her math test is 17/20. If the probability that Andrea studies is 15/16, find the probability that Andrea passes her mathematics test, given that she has studied. Express your answer as a decimal rounded to 4 decimal places.

The probability that Sue will go to Mexico in the winter and France in the summer is 0.40. The probability that she will go to Mexico in the winter is 0.60. Find the probability that she will go to France this summer, given that she just returned from her winter vacation in Mexico. Express your answer as a decimal rounded to 4 decimal places.

A family that is known to have two children is selected at random from among all families with two children. Find the probability that both children are boys, given that there is a boy in this family. Express your answer as a decimal rounded to 4 decimal places.

A die is tossed. Find P(less than 5 l even). Express your answer as a decimal rounded to 4 decimal places.

A number is selected at random from the set {1, 2, 3, 4, 5, 6, 7, 8}. Find P(prime l odd). Express your answer as a decimal rounded to 2 decimal places.

A box contains three blue marbles, five red marbles, and four white marbles. If one marble is drawn at random, find P(not red l not white). Express your answer as a decimal rounded to 3 decimal places.

A number is selected randomly from a hat containing all the integers from 10 to 50. Find P(even l greater than 40). Express your answer as a decimal rounded to 1 decimal place.

A coin is tossed. If it shows heads, a marble is drawn form Box 1, which contains one white and one black marble. If it lands tails, a marble is drawn from Box 2, which contains two white and one black marble. Find P(black l coin fell tails). Express your answer as a decimal rounded to 4 decimal places.