Chapter 4

2 events are ________________ if one event happening influences the probability of the other event happening

dependent

outcome

each individual result that is possible for a probability experiment

mutually exclusive

events that have no outcomes in common

experimental probability

if E is an event, the P(E) is where f is the frequency of event E and n is the total # of times the experiment is preformed

classical probability

if all outcomes are equally likely to occur, then P(E), is either: 1: where n(E) is the # of outcomes in the event 2: n(S) is the # of outcomes in S

2 events are _____________________ if one event happening does not influence the probability

independent

with replacement

when objects are placed back into consideration before performing the next stage of a multistage experiment

formula for classical probability

# of outcomes in an event/# of outcomes in sample space

There are 728 identical plastic chips numbered 1 through 728 in a box. What is the probability of reaching in and grabbing 544?

1/728

a ball machine contains 19 green balls, 24 red balls, 20 blue balls, and 21 yellow balls. What is the probability of getting a yellow ball?

21/19+24+20+21= 21/84= 1/4

A coin is tossed 9 times. What is the probability of getting all tails?

2^9= 512 so, 1/512

An 8 sided die has 4 colors. What is the probability of rolling a brown on the next toss? Yellow: 40 Pink: 24 Green: 21 Brown: 42

42/40+24+21+42= 42/127

569 identical chips are numbered 1 through 569. What is the probability of grabbing a number less than 478?

477/569

a dog breeder has 3 litters of puppies. What is the probability of having a puppy with no spots? Black without spots: 5 Red without spots: 8 Black with spots: 6 Red with spots: 4

5+8+6+4=23 5+8= 13 =13/23

addition rule

For any two events, E and F, the probability that E or F occurs is given by the following formula: P{E or F} = P(E) + P(F) - P(E and F)

formula for experimental probability

P(E)= f/n (f- # of times E occurs) (n- # of trials)

event

a subset of outcomes from the sample space

subjective probability

an educated guess regarding the chance that an even will occur

multistage experiment

an experiment with more than one step

probability experiment (trial)

any process with a result determined by chance

Classical or experimental probability? Selecting a 7 from a standard deck of cards

classical probability

law of large numbers

the greater the number of trials, the closer the experimental probability will be to the true probability

conditional probability P(F|E)

the probability of event F occuring given that event E occurs first

sample space (S)

the set of all possible outcomes for a given probability experiment (not the number of outcomes)

without replacement

when objects are not placed back into consideration before performing the next stage of a multistage experiment