In the High School there is around 2500 students, 18% of the students smoke cigarettes.

A) If 2 are selected at random, use a Venn diagram with 2 circles; 1 representing the probability that the first student smokes and 1 representing the probability that the other student smokes. Determine the probability that at least 1 of them smokes cigarettes. (This would be equivalent to the probability that either the first student OR the second student smokes.)

B) Repeat the above analysis when 3 students are selected at random.

Note: These trials would be independent given the large population of students.

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 7.8 cm.

a. Find the probability that an individual distance is greater than 210.00 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 195.70 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

a. The probability is (Round to four decimal places as​ needed.): 0.0548

b. The probability is (Round to four decimal places as​ needed.):

According to the Chronicles of Contrived Statistics (March, 2016), the probability that Elon Musk will offer you a free trip into space in the next month is 40%. The probability that scientists at Area 51 will begin sales of pet aliens in the next month is 26%. Finally, they list that probability of both happening in the next month is 16%. What is the probability that either Elon Musk will offer you a free trip into space or scientists will begin sales of pet aliens in the next month?

Answer in decimal form. Round to two decimal places as needed.

For this project:

Create a game with at least 3 outcomes

Develop a probability table with the outcomes for X and the probability p(X)

Find the expected value and standard deviation

Determine if your game is fair

How could be changed to make it fair or favor the player or "house"?

Run the game 50 times and record each outcome

Compute the empirical probability and compare it against the theoretical probability in #2. Find the average outcome of the 50 trials, and compare against the expected value

Please help ! I am confused with this project.

Assume that females have pulse rates that are normally distributed with a mean of mu equals 76.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (b) below.

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 82 beats per minute.

The probability is __________.

b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 82 beats per minute.

The probability is ___________ .

A student club has 65 members; of these members, 28 are male and 22 are freshmen. Of the males, 10 are also freshmen. Answer the questions below as a fraction in the form numerator/denominator. Hint: it may be useful to create your own cross tabulation table.

What is the probability that a randomly selected student in the club is a freshman?

What is the probability that a randomly selected student in the club is a male or a freshman?

What is the probability that a randomly selected student in the club is male given that the student is a freshman?

What is the probability that a randomly selected student in the club is male and a freshman?

1. In Mr ERIZ’s class, the probability of student who likes Mathematics subject is 0.5 and the probability who likes both Mathematics and Statistics subjects is 0.25.

1. If one student is chosen at random, what is the probability that this student likes Statistics given that he/she also like Mathematics subject?

2. If the probability of students who like Statistics is 0.45, are the events ‘like Mathematics subject’ and ‘like Statistics subject’ independent? Justify your answer.                                                                              

(4 marks)

3. Are the events ‘likes Mathematics’ and ‘likes Statistics’ mutually exclusive? Justify your answer.

Assume that you want to investigate the effects of TV commercials on a product. From the questionnaire survey so far, we know the followings.

1. The probability that a purchaser of the product has watched the TV commercial is A.

2. The probability that a non-purchaser of the product has watched the TV commercial is B.

3. The probability that a customer buys the product is 0.1.

Let A = 0.6 and B = 0.2.

Question: What is the probability that a customer who has watched the TV commercial buys the product? ( Answer in the decimal form, not the fractional form.)

A bag of 30 tulip bulbs contains 13 red tulip​ bulbs, 10 yellow tulip​ bulbs, and 7 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag.

(a) What is the probability that the two randomly selected tulip bulbs are both​ red?

​(b) What is the probability that the first bulb selected is red and the second​ yellow?

​(c) What is the probability that the first bulb selected is yellow and the second​ red?

​(d) What is the probability that one bulb is red and the other​ yellow?