MATH309 - Statistics Week 3 - Homework Deadline Due by the end of Week 3 at 11:59pm, ET. Directions For this assignment, please review the chapter reading and videos for this week. You can use any resource both in this course and in the Internet to answer the questions. Submit your answers in a Word document within the Blackboard folder. Remember that the definition of a probability of an event A is as follows: The probability of event A = P(A) = # of ways event A can occur / Sample Space Please watch the videos below on probability: Video 1: Probability (Part1) Video 2: Probability of Not Happening - Corbettmaths Video 3: Probability with OR (cards in deck) Video 4: Probability \"OR\" and Probabilities Video 5: Probability 'OR' Statement and Addition Rule Please answer each of the below questions and label them and show your work in your Word document. 1. When studying the effect of heredity on height, we can express each individual genotype, AA, Aa, aA, and aa, on an index card and shuffle the four cards and randomly select one of them. What is the probability that we select a genotype in which two components are different? Set it up as Event A 2. A \"standard\" deck of playing cards consists of 52 cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. What is the probability of getting a diamond from a standard deck of playing cards? 3. A typical question on a SAT test requires the test taker to select one of five possible choices: A, B, C, D, or E, because only one answer is correct, if you make a random guess, your probability of being correct 4. 5. 6. 7. is 1/5 or 0.2. Find the probability of making a random guess and not being correct (or being incorrect). If the weather man/woman gives a prediction of a 70% chance of rain tomorrow, what is the probability that it will not rain tomorrow? Set up as Event A The formal addition rules say P (A or B) = P(A) + P(B) - P (A and B) where P (A and B) is thought of as P (A intersection B) and A and B are not disjoint sets. Disjoint sets are collections of data that have no items or points in common. Let event A = {even number on a six-sided die} and event B= {numbers 2, 3, on a six-sided die}. Find P (A or B). Are events A and B disjoint events? For two independent events A and B, you have P (A and B) = P(A) * P(B). If event A = rolling a 2 on the first roll of a six-sided die, and event B = rolling a 2 on the second roll, find P (A and B)? Assume that we have a batch of 200,000 heart pacemakers including 199,950 that are good (G) and 50 that are defective. If two of those 200,000 pacemakers are randomly selected without replacement, find the probability that they are both good i.e., P (first pacemaker is good and the second pacemaker is good) =? Hint: set up events A and B. Remember for event B that because there is no replacement in the selection you must reduce the # of ways for event B to occur by 1 and reduce the sample space by 1 also. 8. Please watch the below video on Type I and Type II Errors. This is related to hypothesis testing. Video: Learn to understand Hypothesis Testing for Type I and Type II Errors Type I and Type II Errors can help you in your hypothesis testing (True or False)? 9. The below data summarizes blood groups and Rh types for 100 people, and answer the question for a and b (20 points) - Consider blood type groups A and type Rh-. If 4 out of the 100 subjects are randomly selected, find the probability that they are all universal donors. Calculate the P (A and Rh-) with replacement. Groups Type O A B AB Rh+ 39 35 8 4 Rh- 6 5 2 1 10. The below data summarizes blood groups and Rh types for 100 people, and answer the question for a and b (20 points) - Consider blood type groups AB and type Rh-. If 4 out of the 100 subjects are randomly selected, find the probability that they are all universal donors. Calculate the P (AB and Rh-) without replacement. Groups Type O A B AB Rh+ 39 35 8 4 6 5 2 1 Rh