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Questions and Answers
What is the probability that a student will go to graduate school and take loans to pay for their undergraduate education?
What is the probability that a student will go to graduate school and take loans to pay for their undergraduate education?
0.111
What is the probability that a police officer will give a ticket for speeding?
What is the probability that a police officer will give a ticket for speeding?
0.49
If P(A) = 0.8, P(A OR B) = 0.87, and P(A AND B) = 0.23, find P(B).
If P(A) = 0.8, P(A OR B) = 0.87, and P(A AND B) = 0.23, find P(B).
0.27
What is the probability that a randomly selected friend is in either statistics or writing, but not both?
What is the probability that a randomly selected friend is in either statistics or writing, but not both?
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State the addition rule for probabilities.
State the addition rule for probabilities.
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What is the probability that a randomly chosen friend takes biology or physics, P(B OR P)?
What is the probability that a randomly chosen friend takes biology or physics, P(B OR P)?
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What is P(A AND B) if P(A) = 0.28, P(B) = 0.83, and P(A OR B) = 0.93?
What is P(A AND B) if P(A) = 0.28, P(B) = 0.83, and P(A OR B) = 0.93?
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What is the definition of the addition rule for probabilities?
What is the definition of the addition rule for probabilities?
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Study Notes
Probability Basics
- The probability of a student taking loans for undergraduate education is 0.85.
- The conditional probability of a student attending graduate school given they took loans is 0.13.
- The probability that a student will go to graduate school and take loans is calculated as P(B AND A) = P(B|A)P(A) which equals 0.111 after multiplication.
Mutually Exclusive Events
- A police officer can either give a ticket or a warning; these events are mutually exclusive.
- The probability of a warning is 0.03 and the total probability of giving either a ticket or warning is 0.52.
- To find the probability of giving a ticket, use the formula: P(A) = P(A OR B) - P(B); thus, P(ticket) = 0.52 - 0.03 = 0.49.
Calculating Probabilities
- For events A and B, with P(A) = 0.8, P(A OR B) = 0.87, and P(A AND B) = 0.23, alternative methods can be used to find P(B) by rearranging the addition rule.
Venn Diagrams in Probability
- Six friends are categorized into statistics and writing: Pamela and Sam in statistics, Nandini, Elliot, and Jill in writing, and Matt in both.
- The probability of selecting a friend in either statistics or writing but not both accounts for 5 out of 6 friends.
Addition Rule for Probabilities
- The general formula for finding the probability of either A or B occurring is: P(A OR B) = P(A) + P(B) - P(A AND B).
Real-Life Application of Probability
- Given the probabilities of friends enrolling in classes: P(B) = 1/3 for biology, P(C) = 1/2 for chemistry, P(P) = 1/6 for physics, and P(B AND P) = 1/12 for both biology and physics.
- Using the addition rule: P(B OR P) = P(B) + P(P) - P(B AND P) results in a probability of 5/12.
Shift Assignments
- Employees' shifts during busy seasons: P(A) = 0.28 (8 a.m. - 12 p.m.) and P(B) = 0.83 (12 p.m. - 4 p.m.).
- The total probability that an employee is assigned either shift is P(A OR B) = 0.93.
- Calculate P(A AND B) by rearranging the addition rule: P(A AND B) = P(A) + P(B) - P(A OR B) resulting in P(A AND B) = 0.18.
Probability of Events
- The probability of either of two events happening (or both) is given by the addition rule formula: P(A OR B) = P(A) + P(B) - P(A AND B).
Issues with Products
- Probability of a known issue occurring with a new car model: P(A) = 0.1 for issue A.
- Additional context about issue B and its relationship would require further information such as P(A OR B).
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Description
This quiz focuses on probability concepts related to student loans and graduate school enrollment. It includes calculating the combined probability of students taking loans for undergraduate education and attending graduate school. Test your understanding of these statistical principles with this set of flashcards.
