What is discrete probability?
Studies experiments with a finite number of outcomes
What is an experiment?
A procedure that can be repeated
What is an outcome?
The results of an experiment
What is a sample space?
The set of all outcomes
What is an event? (Probability)
A subset of the sample space
What is the sample space for flipping a coin?
{H,T}
What is the sample space for rolling a six sided die?
{1, 2, 3, 4, 5, 6}
What is the sample space for flipping two coins?
{HH, HT, TH, TT}
A lottery consists of drawing 6 numbers, without replacement, from the numbers 1 - 42. A ticket is some set of 6 random numbers between 1 and 42. What is the probability of matching 2 numbers?
The number of possible outcomes is C(42,6) = 5245786 so to match 2 numbers we choose 2 out of the 6 winning numbers, which is C(6,2), and then we choose 4 numbers from the remaining numbers which aren’t on the winning ticket. This means we choose 4 from the remaining 42-6 = 36 so there are C(6,2)xC(36,4) = 883575 ways of matching 2 numbers. To find the probability of matching 2 numbers you divide this by the total number of possible combinations. 883575 / 5245786 = 0.17
What is the formula for p(A|B)?
p(A|B) = p(A∩B) / p(B)
How do we know if 2 events are independent?
Use P(A∩B) = P(A)P(B) or P(A|B) = P(A)
What is the probability of getting 3 heads in a row when flipping a fair coin?
0.5 x 0.5 x 0.5 = 0.125
If a family has two children and the older child is a girl, what is the probability both children are girls?
1/2
If a family has two children and at least one is a girl, what is the probability both are girls?
1/3
What is a random variable?
A function from the set of outcomes to the set of real numbers. It is NOT a variable.
How do you write the distribution of a random variable X?
P(X=r) = …
What is a Bernoulli random variable?
In a sample space with two outcomes a Bernoulli random variable assigns a value of 1 to one outcome and 0 to the other.
What is the Bernoulli distribution?
f(k) =
{p(X = 1) = p
{p(X = 0) = 1−p = q
What is the nicer expression for the Bernoulli distribution?
f(k) = pᵏ (1−p)¹⁻ᵏ where k=0 or 1
When 3 coins are flipped what are the chances of getting exactly 2 heads in a row?
1/4
