可能性(概率)-Probability.ppt

Probability multiplication Probability multiplication Functional safety Engineering - Probability Probability Rules of Probability Types of Event Probability multiplication Probability addition Fault Trees Probability Assignment Probability assigned by two methods: Physical property determination Geometry, physical shape Experimental outcome determination Number of occurrences/Number of Trials Probability is a number : (0 P 1) Probability P(Gold) = 0.8 Event Types Independent – Events that do not affect each other Coin Tosses Dice Throws Complimentary – When one outcome does not occur, the other will always occur Coin Mutually Exclusive – When one event occur the other can not happen Dice Independent Events Events that do not effect each other Tossing of two coins Throwing a pair of dice Failure of one component in a system ? Normally considered independent Complimentary Events Complimentary When one outcome does not occur, the other will always occur Tossing a coin Two events possible – head and tails Success / Failure ? Probability of Complementary Events P(A*) = 1 – P(A) Probability of successful operation for the next year is 0.8. What is the probability of failure the next year ? (0,2) Mutually Exclusive Events Mutually Exclusive When one event occur the other can not happen Toss of one die Outcome of 1,2,3,4,5,6 are mutually exclusive Probability multiplication P(A AND B) = P(A) * P(B) Probability multiplication For Independent events P ( A AND B ) = P (A) * P (B) Probability Addition Mutually Exclusive Events P(A or B) = P(A) + P(B) Probability Addition Mutually Exclusive Events P(A or B) = P(A) + P(B) Roll 1 die. What is the probability of getting a 4 or a 6 ? Probability of getting 4 - 1/6 Probability of getting 6 - 1/6 The probability of rolling 4 OR 6 P(A) + P(B) = 1/6 + 1/6 = 2/6 Probability Addition Independent Events P(A or B) = P(A) + P(B) – P(A AND B) Probability Addition Independent Events P(A or B) = P