1. In New Mexico, 15% of residents are covered by Medicaid. 10% of residents are covered by Medicare. 3% of residents are dual eligible and covered by both Medicare and Medicaid. Draw a Venn Diagram and then calculate the probability that a New Mexico resident selected at random will be covered by either Medicare or Medicaid.

2.  A binomial distribution describes a random variable, X, that has 4 possible outcomes. Outcome 1 has a probability of 25%, Outcome 2 has a probability of 15%, Outcome 3 has a probability of 20%. What is the probability of Outcome 4?

The Accumulative Probability by using Poisson Distribution For four Persson equal 0.172991608 and For Five Person =0.300708276. Compute the fowling:

1- The Probability that we have Five person?

2- The Probability that we have Five person at Most?

3- The Probability that we have less than Five person?

4- The Probability that we have more than Five person?

5 – If the Mean = 0.5 Compute that we Have 2 Person at Most?

6 - If the Mean = 1.5 Compute that we Have 2 Person at least?

A fire alarm system inside an office building has two types of activation devices, A and B, which operate independently.
Probability that device A is turned on in the case of a fire is 0.97.
Probability that device B is turned on in the case of a fire is 0.85.
When there is a fire, the fire alarm system is turned on when at least one of two activation devices is turned on.

Probability that both devices are turned on in the case of a fire is_____________
Probability that the fire alarm system is turned on in the case of a fire is _____________
Probability that the fire alarm system is not turned on in the case of a fire is ___________

Many businesses apply the understanding of uncertainty and probability theory in their decision practices in their business. Probability models can greatly help businesses to optimize their policies and make safe decisions. Although complex, these methods of probability can increase profitability and business success.

Please, develop and explain a situation where you would apply probability theory, or specify a probability distribution. Mention and explain the reason for his selection, and the advantages and disadvantages of the use of probabilities are in your example. Try to explain it in 200-250 words. Formulas and numbers are welcome and needed.

Jim, a young baseball player has a 40% chance of getting a hit when he comes up to bat during a game. If he comes to bat 5 times during the next game then: This is binomial probability question

i) What is the probability that he gets a hit exactly 2 times in the game. ii) What is the probability that he gets at most 4 hits in the game.
iii) What is the probability that he does not get a hit in the game.
iv.) What is the probability that he get at least 4 hits in the game

3. Consider the following problem : It is known that 25% of a planet is land and 75% of it is water. If 10 meteors are heading towards the planet, what is the probability that they all miss land and crash into the water? Design an experiment to determine this probability using a nickel and a dime. (A)

4.The probability of having three boys out of four children is to be determined. A simulation is conducted in which the experimental probability is exactly equal to the theoretical (actual) probability. If the event occurred 53 times during trials, how many trials were conducted? (T/I)

What is the probability that you would get heads-up when flipping a coin ONE time?

What is the probability that you would get heads-up when flipping a coin TEN times?

What is the probability that you would get heads-up on two coins flipped at the same time?

What is the probability that you would roll a 5 on a single dice if you rolled it five times?

What is the probability that you would roll a 3 on a single dice if you rolled it five times?

1.a We have 12 dice: 8 are regular and 4 are irregular. The probability of getting a 3 with an irregular dice is twice the probability of anyone of the rest of the numbers. 1) Find the probability of getting a 3 2) If we have got a 3, find the probability of being tossed with a regular dice 3) Find the probability of getting a 3 with an irregular dice (0.8 points)

1.b Which one is true and why? P(A|B) + P(B|A) = 1 or P(A|B) + P(Ac|B) = 1 (0.2 points)

Question 8 A factory uses a diagnosis test whether a part is defective or not. This test has a 0.90
probability of giving a correct result when applied to a defective part and a 0.05 probability
of giving an incorrect result when applied to a non-defective part. It is believed that one
out of every thousand parts will be defective.

(a) Calculate the posterior probability that a part is defective if the test says it is defec-
tive.
(b) Calculate the posterior probability that a part is non-defective if the test says it is
non-defective.
(c) Calculate the posterior probability that a part is misdiagnosed.

A poll is given, showing 75% are in favor of a new building project. If 138 people are chosen at random, answer the following. What is the probability that exactly 103 of them are in favor of a new building project? What is the probability that less than 103 of them are in favor of a new building project? What is the probability that more than 103 of them are in favor of a new building project? What is the probability that exactly 110 of them are in favor of a new building project? What is the probability that at least 110 of them are in favor of a new building project?