Suppose the probability of success in a binomial trial is 0.63. What is the probability of failure? О А. 0.77 В. 0.23 С. 0.63 D. 0.37

Jack wants to take Deep Learning or Spanish, or both this semester. He is applying for enrolment. The chance of getting into a Deep Learning course is 50%, and getting into a Spanish course is 40%. Getting into both is 20%.  If he applies for both Deep Learning and Spanish classes, what is the probability that he will enrol in either or both of the classes?

A random sample of two Americans is selected. What is the probability that both will have type O blood?

Suppose that the test score of a student taking the final of a probability course is a random variable with mean 80. (a) Give an upper bound for the probability that a student's test score will exceed 90. P{score > 90} < (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 30. What can you say about the probability that a student will score between 70 and 90 (do not use the central limit theorem)? P{70 < score < 90} ? (c) How many students would have to take the final to ensure with a probability of at least 0.95 that the class average would be within 3 of 80 (do not use the central limit theorem)? n = (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? п —