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In Exercises 1–22, use Bayes’ theorem to calculate the probabilities.
Mathematics Exam In a calculus course, the instructor gave an algebra exam on the first day of class to help students determine whether or not they had enrolled in the appropriate course. Eighty percent of the students in the class passed the exam. Forty percent of those who passed the exam on the first day of class earned an A in the course, whereas only twenty percent of those who failed the exam earned an A in the course. What is the probability that a student selected at random passed the exam on the first day of class, given that they earned an A in the course?
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- One hundred people were surveyed, and one question pertained to their educational background. The results of this question and their genders are given in the following table. Female (F) Male (F′) Total College degree (D) 30 20 50 No college degree (D′) 30 20 50 Total 60 40 100 If a person is selected at random from those surveyed, find the probability of each of the following events.1. The person is female or has a college degree. Answer: equation editor Equation Editor 2. The person is male or does not have a college degree. Answer: equation editor Equation Editor 3. The person is female or does not have a college degree.arrow_forwardPlease draw a detailed grapharrow_forwardFor allarrow_forward
- not use ai pleasearrow_forward3) Let G be the group generated by elements a and b satisfying the relations a² = 63, 66 = 1, and a ¹ba = b¹. Which of the following is equivalent to the element z = a a-2ba3b3? A) b-2a-1 B) ab² C) ab D) ba E) b²aarrow_forward1) Find all complex solutions to cos(z) =arrow_forward
- 3) Compute where C is the circle |z― i| = - 1 2 2+1 Po z z - 2)2 dz traversed counterclockwise. Solution: TYPE YOUR SOLUTION HERE! INCLUDE A SKETCH OF THE COM- PLEX PLANE AND THE CURVE C. ALSO, MARK ALL SINGULARITIES OF THE INTEGRAND!arrow_forward2) Consider the function f (z = re²) = e cos(In(r)) + ie¯* sin(ln(r)). Show that is holomorphic at all points except the origin. Also show that =arrow_forward3) If a is a positive number, what is the value of the following double integral? 2a Love Lv 2ay-y² .x2 + y2 dadyarrow_forward
- 2) Consider the set SL(n, R) consisting of n x n matrices with real entries having de- terminant equal to 1. Prove that SL(n, R) is a group under the operation of matrix multiplication (it is referred to as the Special Linear Group).arrow_forward1) What is the parity of the following permutation? (1389) (24) (567)arrow_forward4.7 Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h²) to estimate the first derivative of the function examined in Prob. 4.5. Evaluate the derivative at x = 2 using a step size of h = 0.2. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
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