MAT 232 WEEK 2 COMPLETE STUDY GUIDE
WITH SOLVED QUESTIONS
◉ Blank is any process that can be repeated over and over. We often
assign probabilities to these.
Answer: Experiment
◉ Blank is the result of an experiment.
Answer: Outcome
◉ Blank is a listing of all possible outcomes of a probability
experiment.
Answer: Sample space
◉ Blank is a collection of outcomes from a probability experiment. It
could be a single outcome or multiple outcomes. In probability we
call this P(E).
Answer: Event
◉ Example: suppose a probability experiment involved throwing a
die one time
A) identify the outcomes
,B) determine the sample space
C) list the outcomes for E= "roll an even number".
Answer: A){ 1, 2, 3, 4, 5, 6}
B){ 1, 2, 3, 4, 5, 6}
C){2, 4, 6}
◉ Example: list the sample space if a letter (A B C D) were selected
and a spinner contained the number 1, 2, and 3..
Answer: {A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3}
◉ Probability rules:
1) each event P(E) must have a probability that is some value
between blank and blank
-This implies that probabilities cannot ever be blank or
(greater/lesser) than 1.
2) the sun or probabilities for al possible outcomes in the sample
space must sum to be blank.
3) if an event is impossible it's probability is blank. P(E)= blank
4) if an event is certain to occur P(E)= blank
5) in general any event with a probability of less than 0.05 would be
deemed blank.
Answer: 1) 0 and 1
-negative or greater than
,2) 1
3)0,0
4) 1
5)unusual
◉ an experiment is a blank probability or experiment if each
outcomes is equally likely.
Answer: Classical
◉ What probability is this?
Example: tossing a coin, rolling a die, drawing a card from a deck.
Answer: Classical
◉ To find probability, blank the number of outcomes which satisfy
the event by the number of outcomes in the sample space..
Answer: Divide
◉ Example:
What is the probability of getting an even number when you throw
the die one time?
What happens if the number of die increases to two? Does this still
qualify as a classical probability experiment?.
, Answer: 1/2 or 0.50
No. Rolling two dice instead of just one results in a sample space
where the outcomes are not all equally likely
◉ Probabilities based on evidence (data) that have been observed
are called blank. Can be though of relative frequencies..
Answer: Empirical probabilities
◉ If we toss a coin one time that is a classical experiment. If we toss
a coin 25 times and count the number of heads, then we have blank
evidence about the pro imita a head will be observed using this coin.
In the long run the probability will approach the theoretical value of
0.500 by the blank.
Answer: Empirical
law of large numbers
◉ Example: an insurance agent currently insures 192 teenage
drivers. Last year, 24 of those drivers had to file a claim for an
accident. Given this info what is the probability that in a given year a
teenager will have to file an insurance claim?.
Answer: 0.125
WITH SOLVED QUESTIONS
◉ Blank is any process that can be repeated over and over. We often
assign probabilities to these.
Answer: Experiment
◉ Blank is the result of an experiment.
Answer: Outcome
◉ Blank is a listing of all possible outcomes of a probability
experiment.
Answer: Sample space
◉ Blank is a collection of outcomes from a probability experiment. It
could be a single outcome or multiple outcomes. In probability we
call this P(E).
Answer: Event
◉ Example: suppose a probability experiment involved throwing a
die one time
A) identify the outcomes
,B) determine the sample space
C) list the outcomes for E= "roll an even number".
Answer: A){ 1, 2, 3, 4, 5, 6}
B){ 1, 2, 3, 4, 5, 6}
C){2, 4, 6}
◉ Example: list the sample space if a letter (A B C D) were selected
and a spinner contained the number 1, 2, and 3..
Answer: {A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3}
◉ Probability rules:
1) each event P(E) must have a probability that is some value
between blank and blank
-This implies that probabilities cannot ever be blank or
(greater/lesser) than 1.
2) the sun or probabilities for al possible outcomes in the sample
space must sum to be blank.
3) if an event is impossible it's probability is blank. P(E)= blank
4) if an event is certain to occur P(E)= blank
5) in general any event with a probability of less than 0.05 would be
deemed blank.
Answer: 1) 0 and 1
-negative or greater than
,2) 1
3)0,0
4) 1
5)unusual
◉ an experiment is a blank probability or experiment if each
outcomes is equally likely.
Answer: Classical
◉ What probability is this?
Example: tossing a coin, rolling a die, drawing a card from a deck.
Answer: Classical
◉ To find probability, blank the number of outcomes which satisfy
the event by the number of outcomes in the sample space..
Answer: Divide
◉ Example:
What is the probability of getting an even number when you throw
the die one time?
What happens if the number of die increases to two? Does this still
qualify as a classical probability experiment?.
, Answer: 1/2 or 0.50
No. Rolling two dice instead of just one results in a sample space
where the outcomes are not all equally likely
◉ Probabilities based on evidence (data) that have been observed
are called blank. Can be though of relative frequencies..
Answer: Empirical probabilities
◉ If we toss a coin one time that is a classical experiment. If we toss
a coin 25 times and count the number of heads, then we have blank
evidence about the pro imita a head will be observed using this coin.
In the long run the probability will approach the theoretical value of
0.500 by the blank.
Answer: Empirical
law of large numbers
◉ Example: an insurance agent currently insures 192 teenage
drivers. Last year, 24 of those drivers had to file a claim for an
accident. Given this info what is the probability that in a given year a
teenager will have to file an insurance claim?.
Answer: 0.125
