32. You roll two six-sided fair dice.

a. Let A be the event that either a 3 or 4 is rolled first followed by an odd number. P(A) = Round your answer to four decimal places.

b. Let B be the event that the sum of the two dice is at most 7. P(B) = Round your answer to four decimal places.

c. Are A and B mutually exclusive events?

• No, they are not Mutually Exclusive
• Yes, they are Mutually Exclusive

d. Are A and B independent events?

• They are not Independent events
• They are Independent events

33. An experiment consists of first rolling a die and then tossing a coin:

a. How many elements are there in the sample space?

b. Let A be the event that either a 1, 2, 3 or 4 is rolled first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal rounded to four decimal places.

c. Let B be the event that an even number is rolled, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive?

• Yes, they are Mutually Exclusive
• No, they are not Mutually Exclusive

34. A and B are independent events. Use the following probabilities to answer the question. Round to 4 decimal places.

P(A) = 0.34, P(A and B) = 0.21, find P(B)

P(B) =

35.

J and K are independent events.P(J | K) = 0.79. Find P(J)

P(J) = ____

36.

Suppose that you have 9 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?

• _____They are independent events
• _______They are dependent events

____37.

Suppose that you have 5 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?

• _____They are independent events
• ______They are dependent events

38.

At a drug rehab center 37%experience depression and 28%experience weight gain. 15% 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?

• yes
• no

e. Are depression and weight gain independent?

• no
• yes

____