1.9) A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 5 digits long, and that each digit could be a number between 0 and 6. Assume that the hacker makes random guesses. What is the probability that the hacker guesses the password on her first try? Round to six decimal places. Probability =

2.10) You roll two six-sided fair dice.

a. Let A be the event that either a 4 or 5 is rolled first followed by an even 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 5. 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

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

P(A) = 0.63, P(A and B) = 0.51, find P(B)

P(B) =

4.12) J and K are independent events.P(J | K) = 0.87. Find P(J)

P(J) =

5.13) Suppose that you have 10 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

6.14) 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