PROBABILITY Flashcards
What is probability?
The likelihood of an event happening.
What is the the difference between theoretical and experimental probability?
theoretical is from thinking of all of the possibilities and doing it with math, experimental is the #successes/total attempts you observe.
how do you find “probability”
(# ways you can be successful) / (# total ways possible)
What is the symbol that joins two sets together into one set?
A big U , stands for UNION
What is the symbol that just takes the overlap of two sets?
An upside down U, look like this: ∩, INTERSECTION
What do students forget about OR ?
The OR BOTH part. The union of A and B are all of the elements in A, in B and also the ones that are in BOTH.
Why does OR go with UNION, ex. A U B = A or B
Because you are part of the union as long as you are a part of A or B or BOTH.
Why does AND go with INTERSECTION? A ∩ B = A and B
Because ONLY if you are a member of A and also a member of B, can you be a part of the intersection, A ∩ B
OR goes with______ [union or intersection]
union
AND goes with ______ [union or intersection]
intersection
UNION goes with ______ [OR or AND]
OR
INTERSECTION goes with _____ [OR or AND]
AND
What numbers can represent a probability?
Always between 0 and 1, examples: 0, .75, .05, 1, .35
What fractions can represent a probability?
Any fraction as long as the top is smaller than the bottom (or equal). IT CAN’T BE TOP HEAVY!
Can you have a probability of 3.5?
NO. probabilities are between 0 and 1
can you have a probability of 0.5?
Yes, that’s 50%
can you have a probability of 3/5?
Yes, that’s 60%
can you have a probability of 5/3?
NO… that is more than 1
How can you think of %
PER 100 (or, divided by 100)
If you have 3 pairs of shoes, two pairs of pants and 4 shirts.. how many outfits?
3*2*4= 24 outfits
How many cards in a deck of cards?
52
How many diamonds in a deck of cards?
13
What is the probability of randomly taking one card and getting a diamond from a deck?
13/52 or 1/4
What is the probability of randomly taking one card and getting a king from a deck?
4/52 or 1/13
What is the probability of randomly taking one card and getting a red card from a deck?
26/52 or 1/2
How many kings in a deck of cards?
4
what is the probability of getting 3 tails in a row flipping a coin?
1/2 x 1/2 x 1/2 = 1/8
What does A’ mean?
The elements not in A
If A = { 1, 2 }, how many elements does A have?
two
If A = { 1, 2, 6} , what is n(A) ?
the number of elements in A. In this case, n(A)= 3
Difference between a Permutation and a Combination?
Permutation is choosing and Placing in a Particular Place, Combinations are just choosing
where is the permutation button on the calculator?
Math > PRB then down to nPr
where is the combination button on the calculator?
Math > PRB then down to nCr
if there are 10 kids and you are choosing 3 to bring on a trip, how many ways can you do that?
Combination. nCr with n=10 and r=3
If there are 10 kids and you are choosing a president, vp and treasurer, how many ways can you do that?
Permutation. nPr with n=10 and r=3
With tree diagrams, what does MA.AD stand for?
Multiply across, Add down
What do the probabilities on the branches leaving a single node in a tree diagram have to add to?
- If you have two branches, then they should add to 1, if you have five branches from same node, all five added together should equal 1.
How do you get the probability of taking a certain route on a tree diagram?
multiply the branches along the path till the end. write it at the end of the branch.
when you are given a two way table, what should you always do?
PUT IN THE TOTALS ON SIDE and BOTTOM and the OVERALL TOTAL IN THE CORNER
What is a way to help shading in VENN diagrams?
Label the areas 1, 2, 3 and 4. Let A= {1,2} B= {2,3} , intersection is {2} and outside of the circles {4).
When you shade a VENN diagram, what does A U B look like?
Both circles and the overlap are all shaded (everything inside)
When you shade a VENN diagram, what does A ∩ B look like?
Just the overlap sliver in the middle is shaded.
What does (A’)’ look like when shading?
double negative. (A’)’ = A, so the entire A circle should be shaded.
What does (A U B)’ look like when shading?
shade just the area outside of the circles.
change the probability of 1/3 to a decimal and a percent
about .33 or 33% (.33333333333)
change the probability of 2/3 to a decimal and a percent
about .67 or 67% (.66666666666)
change the probability of 1/2 to a decimal and a percent
0.5 or 50%
change the probability of 1/4 to a decimal and a percent
0.25 or 25%
change the probability of 3/4 to a decimal and a percent
0.75 or 75%
change the probability of 1/5 to a decimal and a percent
0.2 or 20%
change the probability of 2/5 to a decimal and a percent
0.4 or 40%
change the probability of 3/5 to a decimal and a percent
0.6 or 60%
change the probability of 4/5 to a decimal and a percent
0.8 or 80%
change the probability of 1/8 to a decimal and a percent
0.125 or 12.5%
change the probability of 1/10 to a decimal and a percent
0.1 or 10%
change the probability of 0.45 to a percent
45%
change the probability of 6% to a decimal
0.06
change the probability 0.0003 to a percent
0.03%
change the decimal 0.3 to a fraction
3/10
change the decimal 0.03 to a fraction
3/100
change the decimal 0.003 to a fraction
3/1000
change the decimal 0.0003 to a fraction
3/10000
change the probability 0.04% to a decimal
0.0004
change the probability 0.04 to a percent
4%
change the probability 0.5% to a decimal
0.005
change the probability 40% to a decimal
0.4
change the probability 5% to a fraction
1/20 (one out of 20)
one out of five is ____ or ____%
0.20 or 20%
one out of ten is _____ or ____%
0.1 or 10%
three out of ten is ____ or ____%
0.3 or 30%
one out of twenty is ____ or _____%
0.05 or 5%
one out of four is _____ or ____%
0.25 or 25%
one out of three is ____ or ____%
about .33 or 33%
two out of three is ____ or ____%
about .66 or 66%
two out of five is ____ or ____ %
0.4 or 40%
three out of five is ____ or ____%
0.6 or 60%
four out of five is ____ or ____%
0.8 or 80%
change the probability 0.8 to a percent and a fraction
80% and 4/5
what are the decimal equivalents of these popular fractions: 1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000
0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001
What are the fractional equivalents of these popular decimals: 0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001
1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000
What are the fractional equivalents of these popular percents: 50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%
1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000
What are the decimal equivalences of these popular percents? 50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%
0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001
How can centimeters and a meter stick help you think of percent?
Think of centimeters as “PERCENTIMETERS”.. each one is one percent of a meter. 35cm is 35% of a meter.
Can you have a percent of 5/4?
.
YES! that would be 125%….. (this can’t be a probability)
how can you think of 150% of something?
150% of a pizza is one and a half pizzas!! (this can’t be a probability)
can you have more than 100% of something?
YES…. if you have more than a whole. (but this can’t be a probability)
change the decimal 0.3 to a percent.
30%
change the decimal 0.03 to a percent.
3%
change the decimal 0.003 to a percent.
0.3%
change the decimal 0.0003 to a percent.
0.03%
how could you change 25/52 into a decimal?
use your calculator, just divide: 25/52=
(multiply by 100 to get the percent)
If you have a decimal and want the percent, what can you do on your calculator?
multiply the decimal by 100. that will give you the percent.
If you have a percent and want the decimal, what can you do?
on your calculator, divide the percent by 100 and you will get the decimal.
if you have a percent, like 32% and want a fraction, what can you do?
just write it over 100..
so 32% = 32/100
or “thirty-two hundredths”
