Probability Math and Probabilities Worksheet Complete the following exercises. Solutions should be your own, reflect your understanding of the problem and

Probability Math and Probabilities Worksheet Complete the following exercises. Solutions should be your own, reflect your understanding of
the problem and be handwritten. Show all your work and circle/highlight your answers. 1. The registrar reported that among 1500 students, 640 did not register for either a math or English
course, 520 registered for an English course, and 360 registered for both types of courses.
Define the sets as follows: U = {x | x is a student},
M = {x | x registered for a math course},
E = {x | x registered for an English course}
a. Using set notation, write the following sets:
i. (2 pts) “Students who registered for a math course or an English course”
ii. (2 pts) “Students who registered for a math course and an English course”
iii. (2 pts) “Students who registered for a math course and not an English course”
iv. (2 pts) “Students who did not register for a math course or an English course”
b. Create a Venn diagram for the problem and use it to answer the following:
i. (2 pts) How many students registered for an English course and not a math
course?
ii. (2 pts) How many students registered for a math course?
c. What is the probability that:
i. (2 pts) A student registered for both a math course and an English course?
ii. (2 pts) A student registered for a math course?
iii. (2 pts) A student registered for a math course or an English course?
iv. (2 pts) A student registered for exactly one of the two types of courses?
2. Three machines turn out all the products in a factory, with the first machine producing 15% of
the products, the second machine 20%, and the third machine 65%. The first machine produces
defective products 4% of the time, the second machine 10% of the time and the third machine
17% of the time.
a. (2 pts) What is the probability that a defective product was produced at the factory
given that it was made on the third machine?
b. (2 pts) What is the probability that a non-defective product was produced at the factory
given that it was made on the first machine?
C. (4 pts) What is the probability that a defective product was produced at the factory?
d. (4 pts) What is the probability that a non-defective product was produced at the factory?
e. (4 pts) What is the probability that a defective product came from the third machine?
f. (4 pts) What is the probability that a non-defective product came from the first machine?

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