Discrete Mathematics Problem. Please give me just answer no need explanation. Just right answer. Answer like 1. a 2. b like that.

Question 1: Which of the following is NOT a probability distribution?

a) Flip a coin and record the side (head or tail) that faces up.

P(head)=0.2 and P(tail)=0.8.

b) Toss a die and record the side (1/2/3/4/5/6) that faces up.

P (1) =P (2) =P(3)=P(4)=0.2 and P(5)=P(6)=0.1.

c) Weather forecast for tomorrow.

P(rain)=P(cloudy)=0.4 and P(neither)=0.2.

d) Ask a person in College X if he/she majors in computer science.

P(yes)=0.7 and P(no)=0.5.

Question 2: Randomly draw 5 cards out a deck. What is the probability that the 5 cards include exactly one Ace and exactly two Kings?

a) 4?4?3?44?43 / C(52, 5)

b) C(4, 1) C(4, 2) / C(52, 5)

c) C(4, 1) C(4, 1) C(44, 3) / C(52, 5)

d) C(4, 1) C(4, 2) C(44, 2) / C(52, 5)

Question 3: There are 10 people in a room. Assume their birthdays are random. Which of the following is FALSE?

a) The probability that at least one person was born on a Monday is (1 ? 6¹⁰ / 7¹⁰)

b) By the Pigeon Hole Principle, there must be at least two people born on the same day of the week.

c) The probability that all 10 were born on a Tuesday is 1 / 7.

d) The probability that no one was born on a Monday is 6¹⁰/ 7¹⁰

Question 4: Of all the patients in Hospital X, 15% smoke cigarettes. Of those patients who are 65 years or older, 25% smoke cigarettes.

E=patients who smoke cigarettes F=patients who are 65 years or older.

Which of the following is TRUE?

a) E and F are independent.

b) P(E|F) = 25%

c) P(F)=15%.

d) P(F|E) = 15%

Question 5: Company X has 12 workers and 4 of them are from an ethnic minority. There are 3 jobs that nobody likes. If jobs are randomly assigned, what is the probability that all the 3 bad jobs are assigned to workers from the ethnic minority?

a) C(4, 3) / C(16, 3)

b) P(4,3) / P (12,3)

c) 3/16

d) None of the three.

Question 6: You toss two dice in a game. Suppose you will win if the total of the two dice is 10 or higher. Suppose you toss one die at a time, and your first die gets a 5.

E=you are winning the game F=your first toss gets a 5.

Which of the following is TRUE?

a) E and F are independent. In other words, your winning chance doesn't get better or worse after your first die gets a 5.

b) None of the three.

c) P(E) = 4/36

d) P(E|F) = 2/6