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Question: 1 out of five programs three were written by student...

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1. Out of five programs, three were written by Student A. If three programs are randomly chosen for testing (without replacement), calculate the probability that all three of them were written by Student A. List the outcomes in the sample space.
2. Amid students in a certain Capstone group, 60% have taken Linear Algebra , 50% have taken Calculus 3 , and 30% have taken both. What portion of the students…
a. did not take Calculus 3?
b. did not take either Linear Algebra or Calculus 3 ?
c. took Linear Algebra but not Calculus 3 ?
d. took Calculus 3 but not Linear Algebra ?
e. If someone took Calculus 3 , what is the probability that he/she took Linear Algebra too?
f. If someone took Linear Algebra , what is the probability that he/she took Calculus 3 too?
3. A Java program is tested by 4 independent tests. When there is an error, these tests will discover it with probabilities 0.1, 0.2, 0.3 and 0.4, respectively. Suppose that the program contains an error. What is the probability that it will be found by at least one test?

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