Empirical Classical Probability - Addition Rule1 point possible (ungraded)At a teaching seminar there are 8 math teachers, 6 computer science teachers, 5 statistics teachers and 3 Spanish teachers. If an instructor is selected at random, find the probability of selecting a math or Spanish teacher. Round your answer to two decimal places.

Two teaching methods, A and B, are implemented for learning Spanish. There is a 70% chance of successfully learning Spanish if method A is used, and a 85% chance of success if method B is used. However, method B is substantially more time consuming and is therefore used only 15% of the time (method A is used the other 85% of the time). The following notations are suggested:A—Method A is used.B—Method B is used.L—Spanish was learned successfully.A person learned Spanish successfully. What is the probability that he was taught by method A? 0.85 * 0.70 = 0.5950 0.70 (0.15 * 0.85)/(0.85 * 0.70 + 0.15 * 0.85) = 0.1765 (0.85 * 0.70)/(0.85 * 0.70 + 0.15 * 0.85) = 0.8235 (0.85 * 0.70)/(0.70 + 0.85) = 0.3839

Identify which of the following are examples of empirical probability and which are examples of theoretical probability.Emily determines that the probability of the next 4 babies born at the hospital, all being girls, is 1/16.Fred determines, based on facts, that there were 250,653 high school wrestlers last year and only 7,075 NCAA wrestlers in colleges. There is about a 2.8% probability of a high school wrestler going on to wrestle in college.Greg determines that the probability of guessing correctly on one multiple choice question with 5 answers is 20%Select the most correct response about the three examples. Group of answer choicesEmily and Greg gave examples of theoretical probability. Fred gave an example of empirical probabilityEmily, Fred, and Greg gave examples of theoretical probability.Emily, Fred, and Greg gave examples of empirical probabilityEmily and Greg gave examples of empirical probability. Fred gave an example of theoretical probabilityEmily and Greg gave examples of probability. But Fred's story was not an example of probability.

It is known that 10% of Year 12 students in a large country study advanced mathematics.A random sample of n students is selected from all Year 12's in this country, and the randomvariable X is the number of those in the sample who study advanced mathematics.(a) Describe the distribution of X. (1marks)(b) If they select 20 students, determine the probability thatNone of the students in the sample study advanced mathematics. (1 mark)If ten random samples of 20 students are selected, determine the probability that at least one ofthese samples has no students who study advanced mathematics. (2 marks)X 0 1 2 3𝑷(𝑿 = 𝒙) 𝟒𝒂𝟐𝟔𝑎2 − 𝑏2 𝑏2 0.5

In a school, 30 % of the students study math and science, 70 % of the students study science. What is the probability of students studying math, given that the student is already studying science.a42.8%42.8%b23.33%23.33%c40%40%d63.8%63.8%

In a group of students, 10 like mathematics, 8 like science, and 5 like both subjects. If a student is chosen randomly, what is the probability that the student likes only mathematics? a. 2/10 b. 7/13 c. 5/13 d. 6/10