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Probability

Probability. Notes and Questions on Chapters 13,14,15. Sample Space. The Sample Space , denoted S, of an experiment is a listing of all possible outcomes. The sample space of rolling a die once has 6 elements, that is {1,2,3,4,5,6}

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Probability

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  1. Probability Notes and Questions on Chapters 13,14,15

  2. Sample Space The Sample Space, denoted S, of an experiment is a listing of all possible outcomes. • The sample space of rolling a die once has 6 elements, that is {1,2,3,4,5,6} • The sample space of picking a card from a standard deck has 52 elements since there are 52 cards in a standard deck. • The sample space of rolling a pair of dice once has 36 elements, since each die has 6 faces.

  3. Probability and100% Rule • The probability of a particular outcome or an event, denoted P(E), is the likelihood of the event. • P(E)=Number of ways of getting E divided by Number of all possible outcomes of the experiment • The probabilities of individual outcomes in the sample space S add up to 100%!

  4. Complement Rule • Probability of an event E not happening is therefore • P(not E) = 100% - P(E) • P(at least one) = 100% - P(none) • Remember, 100% = 1. You can use either one, but don’t make the mistake such as 100%-0.4=99.6%; the correct answer should be 0.6.

  5. Or/And Rule • Probability of an event A or an event B happening is given by • P(A or B) = P(A) + P(B) – P(A and B) • Here “A or B” means at least one of A or B happens; “A and B” means both A and B happen.

  6. Addition Rule for Disjoint Events • On the other hand, if there are a number of mutually disjoint (i.e, no two to happen simultaneously) outcomes to an event E, then the probability of E is given by • P(E) = P(Outcome1) + P(Outcome2) + … • Example: Finding the probability of making an A, a B, or a C in a math class. • Example: Finding the probability of rolling a 3 or 4 on a single roll of the die.

  7. Multiplication Rule • If there are a number of steps to the occurrence of an event E, then the probability of the event E is given by • P(E) = P(Step1) * P(Step 2) * P(Step 3) *… • Example: Finding the probability that you roll a 6 first, then a 2, and then a 3 on three rolls of a die.

  8. Checking Independence • Two events A and B are said to be independent if whether A happens or not has no say in the subsequent likelihood of B and vice versa. • If P(A, given B)=P(A) then A and B are independent; • Or, if P(A and B) = P(A)*P(B), then A and B are independent.

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