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The min & max values of Probabilities are what?
- 0 - not possible/0% probability
- 1- definitely possible/100% certain
All probability values lie b/w 0 and 1 inclusive.
What is the formula for a probability of a single event A?
- # of outcomes when A occurs = P(A)
- # of possible outcomes
Mutually Exclusive Events means what? What's the equation?
If they can never occur together. i.e. if one happens it completely eliminates the probability of the other occuring.
Complementary Events means what? What's the equation?
When one and only one outcome must occur. But they can never occur together. i.e. Getting a heads or tails on a flip of a coin.
P(A or B) = 1
They are also mutually exclusive since P(A and B) = 0.
Independent Events means what?
The occurence of one event does not affect the probability of the other occuring.
Dependent Events means what?
The occurence of one event affects the probability of another. Thus when calculating the probability of multiple events, the probability will change with each event.
When determining the probability of one event AND another event (which are independent), what should you do?
- Multiply the two probabilities together.
- P (A and B) = P(A) * P(B)
Ex: 1/106 x 1/106 = 1/1012
When determining the probability of one event AND THEN another event (which are dependent), what should you do?
Take the probabilty of the first event, multiply by the probability of the second event (taking into account the first already occured). Thus likely reducing the total outcomes, likely by 1 for the second event.
When a probability question asks you to calculate the probability of two things happening simultaneously, what should you do?
This means the same as calculating two events that are dependent on each other without reset, thus solve the same. It doesn't matter which occurs first.
Probability of event A * Probability of Event B (after taking into account event A occured).
How do you solve a probability question asking for Event A or B?
Take the probability of each alone, add them, and then subtract the probability of BOTH happening.
ex: P(A or B) = P(A) + P(B) - P(A and B)
1/102 + 1/102 - 1/104 = P(A or B)
On probability questions AND means what? How about OR?
- And = multiply
- Or = add/sub
Quick way to remember Mutually Exclusive means...
Both can't happen
In probability always consider whether BOTH events could occur (are/are not Mutually Exclusive). If so, you need to take that into account if using the General Case Formula.
What is the General Case Formula? And when do you use it?
- Use this formula when considering the probabilty of one event OR another. Whether the events are mutually exclusive plays a role.
- ex: P(A or B) = P(A) + P(B) - P(A and B)
When dealing with a probability of multiple events (i.e. 3+ or an "at least one") that are not mutually exclusive (i.e. all could occur together) it's easier to ...
Find the complimentary event (i.e. the probability of each NOT occuring), and then subtract those from 1.
In regards to a pair question: ex: a pair out of 52 cards, you should ...
Realize it's ANY pair, not a specific one. Then think of each event seperately (as always), then the # of favorable outcomes after the first pick.
- i.e. 52/52 = 1 = first pick (Any card)
- Probability of a pair after first pick = 3/51
- Thus probability of a pair occouring after 2 picks = 3/51
What is the formula for a binomial probability (ex. Heads/tails)?
(1/2)n where n = # of flips
1/2 is the probability regardless of heads or tails or any combo.
When computing the probability of a single event, do you need to know the exact # of outcomes?
No, just need to know the proportion of outcomes when this event occurs to the total # of outcomes.
How do you find the probability of several mutually exclusive events?
Add the # of outcomes of each event and then divide by the total # of possible outcomes.
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