6 1 An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the CLASSICAL APPROACH If A and B are mutually exclusive events with P A 0 70 then P B CANNOT BE LARGER THAN 30 If you roll a balanced die 50 times you should expect an even number to appear ALL OF THESE ARE TRUE every other roll exactly 50 times out of 100 rolls 25 times on average over the long term The collection of all possible outcomes of an experiment is called SAMPLE SPACE Which of the following is an approach to assigning probabilities RELATIVE FREQUENCY APPROACH A sample space of an experiment consists of the following outcomes 1 2 3 4 and 5 Which of the following is a simple event 3 Which of the following is a requirement of the probabilities assigned to outcome Oi 0 i for each P O i 1 If an experiment consists of five outcomes with P O1 0 10 P O2 0 20 P O3 0 30 P O4 0 15 then P O5 is 25 Of the last 500 customers entering a supermarket 50 have purchased a wireless phone If the relative frequency approach for assigning probabilities is used the probability that the next customer will purchase a wireless phone is 10 If two events are collectively exhaustive what is the probability that one or the other occurs CANNOT BE DETERMINED FROM THE INFO If two events are collectively exhaustive what is the probability that both occur at the same time CANNOT BE DETERMINED If two events are mutually exclusive what is the probability that one or the other occurs CANNOT BE DETMERMINED If two events are mutually exclusive what is the probability that both occur at the same time 0 00 If two events are mutually exclusive and collectively exhaustive what is the probability that both occur 0 00 If the two events are mutually exclusive and collectively exhaustive what is the probability that one or the other occurs 1 00 If events A and B are mutually exclusive and collectively exhaustive what is the probability that event A occurs CANNOT BE DETERMINED 1 If two equally likely events A and B are mutually exclusive and collectively exhaustive what is the probability that event A occurs 50 If event A and event B cannot occur at the same time then A and B are said to be MUTUALLY EXCLUSIVE The collection of all possible events is called A SAMPLE SPACE 6 2 Which of the following best describes the concept of marginal probability It is a measure of the likelihood that a particular event will occur regardless of whether another event occurs The intersection of events A and B is the event that occurs when BOTH A AND B OCCUR The probability of the intersection of two events A and B is denoted by P A and B and is called the JOINT PROBABILITY The probability of event A gives event B is denoted by P A B Which of the following is equivalent to P A B P A P B If two events are independent what is the probability that they both occur CANNOT BE DETERMINED If the outcome of event A is not affected by event B then events A and B are said to be INDEPENDENT If A and B are disjoint events with P A 0 70 then P B cannot be larger than 0 30 If P A 0 65 P B 0 58 and P A and B 0 76 then P A or B is 0 47 Suppose P A 0 50 P B 0 75 and A and B are independent The probability of the complement of the event A and B is 1 5 75 625 Which of the following statements is correct if the events A and B have nonzero probabilities A and B cannot be both independent and disjoint A and B are disjoint events with P A 0 20 and P B 0 30 Then P A and B is 0 00 If P A 0 35 P B 0 45 and P A and B 0 25 then P A B is 0 556 If A and B are independent events with P A 0 60 and P A B 0 60 then P B is CANNOT BE DETERMINED If A and B are independent events with P A 0 20 and P B 0 60 then P A B is 0 20 2 If P A 0 25 and P B 0 65 then P A and B is CANNOT BE DETERMINED Suppose X the number of pets owned by a family in the U S The probability distribution of X is shown in the table below X 0 1 2 3 Probability 0 56 0 23 0 12 0 09 Pets Narrative What is the chance that a family owns more than one pet 0 21 Pets Narrative Suppose you choose two families at random What is the chance that they each own one pet That means family A owns a pet and family B owns a pet 0 23 0 23 0 0529 6 3 If P A 0 84 P B 0 76 and P A or B 0 90 then P A and B is 0 70 If P A 0 20 P B 0 30 and P A and B 0 then A and B are mutually exclusive events If P A 0 65 P B 0 58 and P A and B 0 76 then P A or B is 0 47 Suppose P A 0 35 The probability of the complement of A is 0 65 If the events A and B are independent with P A 0 30 and P B 0 40 then the probability that both events will occur simultaneously is 0 12 If events A and B are independent then P A and B P A P B Two events A and B are said to be mutually exclusive if P A and B 0 Which of the following statements is always correct P A 1 P A c If A and B are mutually exclusive events with P A 0 20 and P B 0 30 then the probability that both events will occur simultaneously is 0 If A and B are independent events with P A 0 60 and P B 0 70 then P A or B equals 0 88 If A and B are mutually exclusive events with P A 0 30 and P B 0 40 then P A or B is 0 70 If A and B are any two events with P A 8 and P B A 4 then P A and B is 32 3 If A and B are any two events with P A 8 and P B Ac 7 then P Ac and B is 32 6 4 6 5 Bayes Law and prior posterior probabilities A posterior probability value is a prior probability value that has been modified on the basis of new information Which of the …