1.) Given that P(A)= 0.56, P(B)= 0.63, and P(A ∩ B)= 0.41. Find P(A^c | B^c)

2.) An experiment consists of selecting an urn and then removing a marble from the urn. There are 8 red marbles and 22 blue marbles in Urn 1, and there are 14 red marbles and 5 blue marbles in Urn 2. The probability that Urn 1 is selected is 0.4 and the probability that Urn 2 is selected is 0.6. Find the probability that:

• Urn 2 is chosen and a red marble is drawn.
• A blue marble is drawn, given that Urn 1 is selected.

3.) A survey of 1000 people was conducted and the respondents were asked whether or not they smoke. The results are summarized in the following table:

Male Female

Smoker: 127 66

Non-smoker: 403 404

Find the probability that:

• The person is female, given that the person is a non-smoker.
• The person is male, given that the person is a smoker.