Need help with Probability questions X4.

a) If one of the presidents is selected at random, what is the probability that he or she earns between $100k and $300k? b) What is the probability of selecting someone in the $100k-$300k category, given that he or she is a president of a community college? c) What is the probability of selecting someone who is a president of a university and also earns over $300k? d) Given the list of people earning under $100k, what is the probability that a person selected from the list is a president of a university?

A probability problem is listed.

The manager of an Orange dealership keeps records on customers visiting the store. Records show that 40% of the people visiting the store are female. Thirty-five percent (35%) of the females visiting the store will buy an Orange. The records also point out that 20% of the males visiting the store will buy an Orange. a) What is the probability that the customer coming to the store will buy an Orange? b) What is the probability of a customer buying an Orange given that the customer is a female?

Probability Problem

Suppose used car salesmen tell the truth 2/5 of the time, and 1/3 of the trees in a forest are oak. If 4 used car salesmen say that a certain tree in the forest is oak, what is the probability that the tree is indeed oak. I have not been able to get the correct answer.

Having trouble finding Probability

The manager of an Orange dealership keeps records on customers visiting the store. Records show that 40% of the people visiting the store are female. Thirty-five percent (35%) of the females visiting the store will buy an Orange. The records also point out that 20% of the males visiting the store will buy an Orange. a) What is the probability that the customer coming to the store will buy an Orange? b) What is the probability of a customer buying an Orange given that the customer is a female? Please help!

Probability Problem

Saint Paul's Hospital commissioned an independent study to determine if there was a difference between the quality of care provided by hospital-trained nurses and tertiary-trained nurses. Two hundred nurses were rated as either providing Superior Service (S) or Adequate Service (A). The results are as follows: (See attached file). Are the events H and S independent? Justify your answer mathematically.