Probability Rules
P(A or B) = P(A) + P(B) - P(A and B)
How do you read P(A|B)?
What counting method is used when order matters?
Permutations / nPr
What type of study assigns treatments to subjects?
Experiment
What is the expected value of a random variable?
Long-run average outcome / EV = sum( x * P(x) )
What dos it mean if 2 events are mutually exclusive?
They cannot happen at the same time / P(A and B) = 0
State the conditional probability formula.
P(A|B) = P(A and B) / P(B)
What counting method is used when order does NOT matter?
Combinations / nCr
What is the standard error of a sample mean?
SE = SD / sqrt(n)
If a game has a negative expected value, what does that mean?
You lose money per play on average.
What rule is used to find P(A and B) for independent events?
P(A and B) = P(A) * P(B)
What do you know if P(A|B) = P(A)?
A and B are independent
How many outcomes are in the sample space of rolling two dice?
36
What is the standard error of a sample proportion?
SE = sqrt(p * q / n)
or SE = sqrt( p * (1-p) / n)
A game pays $10 with probability 0.2, and $1 otherwise. What is the expected value?
10(0.2) + 1(0.8) = $2.8
If two events are dependent, how do you find P(A and B)?
P(A) * P(B|A)
If P(A and B) = 0.2 and P(B) = 0.5, find P(A|B)
0.2/0.5 = 0.4
How many ways can you arrange 3 letters from 5 distinct letters (no repeats)?
5P3 = 60
What does a 95% confidence interval mean? (1 sentence)
We are 95% confident the interval contains the true population parameter
A ticket costs $3. You win $10 20% of the time. Should you play? Explain
No, the EV = -1, so you lose money on average.
If P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.3, are A and B independent?
Yes because 0.6 x 0.5 = 0.3
If P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1, find P(A|B)
0.1/0.5 = 0.2
A license plate had 3 letters followed by 2 digits (repetition allowed). How many possible plates are there?
26^3 x 10^2 = 17,576,000
Why does increasing sample size decrease standard error? (1 sentence)
Because n is in the denominator of the formulas, so larger n makes SE smaller.
A game pays $20 with probability 0.1, $5 with probability 0.3, and $0 otherwise. A ticket costs $4. Is this a fair game? Explain
EV = 20(0.1) + 5(0.3) + 0(0.6) = 2 + 1.5 = 3.5.
Since 3.5 < 4, not fair (player loses on average)