1.) Round all answers to 4 decimal places.

a. A bag contains 6 black marbles, 7 blue marbles, and8 yellow marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a black marble and then a yellow marble? ___________

b. A bag contains 7 green marbles, 8 yellow marbles, and6 blue marbles.If two different marbles aredrawn from the bag , what is the probability of drawing first a green marble and then a blue marble? _______________

2.) Use the following probabilities to answer the question. Round to 4 decimal places. P(A)=0.74, P(B)=0.21, P(AandB)=0.05. P(BA)=___________

3.) A jar contains 22 red marbles numbered 1 to 22 and 48 blue marbles numbered 1 to 48. A marble is drawn at random from the jar. Find the probability of the given event. Please enter reduced fractions. (a) The marble is red. P(red)= (b) The marble is odd-numbered. P(odd)= (c) The marble is red or odd-numbered. P(red or odd) = (d) The marble is blue or even-numbered. P(blue or even) =

4.) You roll two six-sided fair dice.

a. Let A be the event that the first die is odd and the second is a 4, 5, or 6. P(A) =______________ Round your answer to four decimal places.

b. Let B be the event that the sum of the two dice is 10. P(B) =______________ Round your answer to four decimal places.

c. Are A and B mutually exclusive events?

d. Are A and B independent events?

5.) Suppose that you have 7 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement.

G₁ = the first card drawn is green G₂ = the second card drawn is green

a. P(G₁ and G₂) = ________

b. P(At least 1 green) = _________

c. P(G₂|G₁) = _________ d. Are G₁ and G₂ independent?

6.) Suppose that you have 10 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement. Round your answers to four decimal places.

G₁ = the first card drawn is green G₂ = the second card drawn is green

a. P(G₁ and G₂) = _________

b. P(At least 1 green) = ____________

c. P(G₂|G₁) = ___________ d. Are G₁ and G₂ independent?

7.) At a drug rehab center 34%experience depression and 28%experience weight gain. 13% experience both. If a patient from the center is randomly selected, find the probability that the patient (Round all answers to four decimal places where possible.)

a. experiences neither depression nor weight gain. __________________

b. experiences depression given that the patient experiences weight gain. _________________

c. experiences weight gain given that the patient experiences depression. _____________(round to 4 decimal places)

d. Are depression and weight gain mutually exclusive?

e. Are depression and weight gain independent?