Answer all Kindly.

27.1% of all new math PhDs were in statistics and 30% of all new math Ph.Ds were woman the probability a new math PhD was a woman given the PhD was in statistics 0.4

a) let S be the event a new math Ph.D. was in statistics and let w be the event that a new math Ph.D. was a woman, write the percentages and probabilities given above as probability or conditional probability statements using these letters

How are your grades? In a recent semester at a local university, 3oo students a: enrolled in both Statistics I and Psychology 1. Of these students, as got an A 4') in statistics, is: got an a in psychology, and 44 got an A in both statistics and E: psychology. Round the answers to four decimal places, as needed. Q E1 d]: (a) Find the probability that a randomly chosen student got an A in E statistics or psychology or both. The probability that a randomly chosen student got an A in statistics or psychology or both is D. ms at: (b) Find the probability that a randomly chosen student did not get an A in statistics. The probability that a randomly chosen student did not get an A In statistics is D. Question 3 P In a group of 120 students, the probability of studying statistics is 0.05. P(X= Let X denote the number of students that study statistics. i. Find the probability that, a. Exactly 2 students study statistics, = 2 -b. At least | student studies statistics. (Give your answers to 3 d.p.) Compute the mean and variance of X.2. a. The probability that Marwan will pass Statistics is A % and the probability that he will pass Mathematics is B %. Suppose passing Statistics is independent from passing Mathematics. What is the probability that: (6 marks) i. Marwan will pass both Statistics and Mathematics? ii. Marwan will pass at least one module (Statistics or Mathematics)? iii. Marwan will fail Statistics? b. Let the events A and B be such that P(A") = A %, P(B) = B %. Find P(A U B), if i. A and B are mutually exclusive. (2 marks) A and B are independent. (2 marks)A college is studying the probability students will take one or more statistics classes. The following probability distribution shows the likelihood students will take 1, 2, 3, 4, or 5 statistics classes. NOTE: This is NOT a Binomial Distribution. What is the standard deviation of this discrete probability distribution? Number of Statistics Classes Probability 60 2 20 3 12 4 04 5 04 Correct Answer Not Provided 0 1.3115 1.0778 1.5811