A
The probability that 2 events will both occur is the called the probability of ________.
Intersection
The probability that one event or another will happen is called the probability of ___________.
Union
You should only play a game when cost is _________.
Less than the expected value of the game.
The probability of the complement of an event is the probability that _________________.
The event will not happen
What is the expected value of rolling a die?
3.5
What is the formula for expected value?
Sum of all of the outcomes multiplied by their probabilities.
How do you calculate total probability of an outcome in a tree diagram?
Multiply along each branch that reaches the outcome.
P(B)
For mutually exclusive events, P(A ∩ B)=__________.
Zero
You flip the fair coin. Every time you get heads, you lose $1, and every time you get tails, you gain $1. Additionally, there is a $0.01 cost to play. Do you play?
Drawing marbles from a bag, and replacing them each time is an example of ____________.
Independent events
If events are independent, P(A ∩ B) =____________.
P(A)*P(B)
You can't roll both a 1 and a 5 on a die at the same time because they are _________________ events.
The belief that a certain random event is less likely or more likely, given a previous event or a series of events is called ___________.
Gambler's Fallacy
Drawing cards from a deck without replacing them is an example of __________.
Dependent events
The Law of Large numbers states that as the number of trials increases, the ________ probability tends towards the ___________ probability.
Experimental, Theoretical
In the Monty Hall problem, we found that switching gives a _____ chance of winning, and not switching gives a _______ chance of winning.
2/3, 1/3
If a bag of balloons consists of 47 white balloons, 5 yellow balloons, and 10 black balloons, what is the approximate likelihood that a balloon chosen randomly from the bag will be black?
16%
In a Venn Diagram, which area is represented by the union of the 2 events?
Everything inside either circle.
You select 2 cards from a deck, without replacement. What is the probability both are black?
.245
At soccer, Coach Sam is coach 60% of the time, and the rest of the time is Coach Alex. With Sam, you are goalkeeper 50% of the time. With Alex, you are goalkeeper 30% of the time. What is the total probability you are goalkeeper? (Use a tree diagram)
42%
An MP3 player is set to play songs at random from the fifteen songs it contains in memory. Any song can be played at any time, even if it is repeated. There are 5 songs by Band A, 3 songs by Band B, 2 by Band C, and 5 by Band D. If the player has just played two songs in a row by Band D, what is the probability that the next song will also be by Band D?
1/3
In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student?
17/30
An urn contains 6 red marbles and 4 black marbles. Two marbles are drawn without replacement from the urn. What is the probability that both of the marbles are black?
2/15 or 0.133
In the rule of addition, why do we subtract the intersection?
Otherwise it will get counted twice.