Knewton Alta Chapter 3 Part 2

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).