Problem 3: In a certain population, 80% drinks, 15% smokes, and 13% both drinks and smokes. A subject is chosen at random from this population. Events: D - Drinks, S - Smokes, DS -Drinks and Smokes (a) Fill in the following blanks and use these values to complete the table belov Probabilities: P(D) Probabilities Smokes (S) Drinks (D) P(S) P(DS) Not Smokes (3) Total P(D) P(D)- 1.00 P(DS) P(DS)- PDS) = P(S) Not Drink (D)P(DS)- P(S) Total (b) What is the probability the person does not drink? (c) What is the probability the person drinks or smokes? (d) If the person drinks, what is the probability that he or she smokes? (e) If the person does not smoke, what is the probability that he or she drinks? (f) Are the events "Drinks" and "Smokes" mutually exclusive? (State Ύes" or No" and explain.) (g) Are the events "Drinks" and "Smokes" independent? (State "Yes" or No" and explain.)

The below was the answer I received when I asked the following question. Dr. Deming’s Red Bead Experiment is an exercise in the laws of probability. The workers were frustrated because no matter what they did, the outcome was not predictable. If the paddle holds 50 beads and there are 500 white beads and 50 red beads in the box, what is the probability, using one sample, of filling a paddle with 47 white beads and only three red beads? What I need to understand is how did you get the highlighed answers below because these require a factorial of 500 and I have not found anything that will calculate that. Thank you        Step 1 Given Information: Number of white beads = 500  Number of red beads = 50  Total number of beads = 550    Step 2 The probability, using one sample, of filling a paddle with 47 white beads and only three red beads can be determined as follows: Probability = C47500*C350C50550=(2.94*10^66) (19600)(3.44*10^71)=0.1675

Please answer both questions please. I'd really appreicate it. Thank you.

Probability is known as one of the most difficult topics in math . Can you give us one reason for that

Approximately 30% of obese patients will develop diabetes. Answer the following questions if a physician sees 10 patients what is the probability that 50 will develop diabetes. once you answer it please show me how to set this up please show me how to set this question up so I can do it