Basic Probabilities
What do you call a number that can't keep still?
A Roamin' Numeral!
Why did the acute angle feel bad?
Because it was never right!
What is this:
(P+L)(A+N)
PA+LA+PN+LN
A Foiled Plan!
Why did zero and two break up?
Because some ONE came between them!
What's the butterfly's favorite subject in school?
Mothematics!
How do you find a basic probability? (explain the basic formula)
"ways to succeed"/"total possible outcomes"
What is the difference between mutually exclusive events and events that are not mutually exclusive?
Mutually exclusive events can't have items or outcomes in multiple categories. Ex: Political Parties.
Not Mutually Exclusive can have overlap. Ex: Cards (a queen and a heart)
If we are selecting items without replacement (in a relatively small sample), how do the probabilities change with every draw?
The total and outcomes chosen go down by one with each draw
What is the general formula to find the probability of A given B?
P(A|B)=(P(Aand B))/(P(B))
What is the difference between a permutation and a combination?
In a permutation order matters, but in a combination it doesn't, so picking A then B is the same as B then A
When a card is drawn from a deck, find the probability of selecting:
a spade
13/52 " or " 1/4
When two events are not mutually exclusive what do we have to do?
Get rid of the overlap
Without replacement, how do the probabilities change when taken from a very large sample? (EX sample of all americans)
The probabilities stay the same as one less person leaves the probability relatively unaffected
What is a good strategy for "at least" problems?
EX: the probability of flipping "at least" 1 head?
Finding the complement (everything not included) and subtracting the probability from 1
A game store sells 15 board games that can be bought in a pack of 4 for a discount. How many ways are there to select 4 games to be able to get the discount?
Order doesn't matter: combination
15C4
1365
When a card is drawn from a deck, find the probability of selecting:
a 3 or a king
4/52+4/52
8/52
There is a 0.78 probability that Sharon will buy a cat and a 0.53 probability that Janice will buy a cat, and a 0.47 probability that both will buy cats. Find the probability that Janice or Sharon will buy a cat.
P(J)+P(S)-P(J and S) (overlap)
0.78+0.53-0.47=.84
A food stand offers pizza, hot dogs and hamburgers. Roughly 4 out of 5 order pizza. 4 people order food. Find the Probability that none order pizza
P(pizza)=4/5
P(no pizza)= 1/5
1/5*1/5*1/5*1/5= 1/625 or 0.0016
A person has a choice of 6 drinks, 3 appetizers, 5 main courses and 2 desserts in a certain meal deal. How many total ways can a person get the meal deal assuming they can only have one from each category?
6*3*5*2
180 ways
In a school there are 14 teachers; 10 women and 4 men. 5 are chosen to attend an ALICE training. Find the probability that 2 men and 3 women will be selected.
(4C2*10C3)/(14C5)
360/1001=0.3596
During a prize drawing, there are 2 blue tickets, 5 yellow tickets and 3 red tickets in a bucket. What is the probability of drawing a blue ticket and winning a prize?
2/10
There is a 0.54 probability that Erika will like a TikTok and a 0.68 probability that Olivia will like a TikTok, and a 0.37 probability that both will like a TikTok. Find the probability that neither will like a TikTok.
"probability Erika or Olivia will like it:"
P(E)+P(O)-P(E and O)("overlap")
.54+.68-.37=.85
"Probability neither will:"
1-.85= .15
"Or use the Venn Diagram idea"
8 purple popsicles 6 red popsicles, and 3 green popsicles are in a box. Two are drawn blindly without replacement. Find the probability of drawing 2 red popsilces.
6/17*5/16=15/136 or 0.1103
The probability of a snowstorm happening and school being cancelled is 0.09. Dustin hears the weather forecast, and there is a 70% chance of a snowstorm tomorrow. Find the probability that school will be cancelled, given that it snows.
(P(S and C))/(P(S))
0.1286
If 80 wonka bars are sold and 3 have golden tickets, find the probability that one person will find 3 golden tickets if that person buys 3 candy bars.
(77C0*3C3)/(80C3)
1/82160=0.000012