The Rule of Odds
A and B are said to be this if
P(A\cap B)=P(A)P(B)
Independent
You have 7 different books and want to choose 3 of them to take on vacation. This is the number of different combinations you can take.
7C3=35
This distribution is known as the "first-success" distribution.
The Geometric Distribution
The formula to find the expected value of a continuous random variable X.
E[X]=\int_-\infty^\inftyxf(x)dx
The accumulation function for compounded interest at an annual effective rate of 4%.
a(t)=(1.04)^t
This rule helps compute the probability of an event by summing over all ways it can occur through a partition of the sample space.
The Law of Total Probability
The probability that exactly one of two selected factory workers is low-risk where there are 25 factory workers, 20 of which are low-risk and five are high-risk.
1/3
For this type of random variable often used to model counts of events in fixed intervals, the variance is equal to the mean.
Poisson
The short-cut formula for variance.
E[X^2]-\mu^2
If you invest $3,000 at time 0, and the accumulation function is a(t)=1+0.04t, this is how much you'll have at time 5.
$3,600
The formula that is used to find
P(A|B)
(P(A\capB))/(P(B))
The value of
P(A)
where
P(A\cup B)=0.7, P(A\cup B^C)=0.9
0.6
The distribution of hurricanes in a 20-year period where
(i) In any calendar year, there can be at most one hurricane.
(ii) In any calendar year, the probability of a hurricane is 0.05.
(iii) The numbers of hurricanes in different calendar years are mutually independent.
Binomial(n=20, p=0.05)
A random variable X is uniformly distributed on the interval [2, 6]. This is the probability that X<4
1/2 or 0.5
If $2,000 is invested under simple interest at an annual rate of 4.5%, this is the amount of interest earned in the fourth year.
90
When A and B are this, the probability of union can be written as
P(A\cup B)=P(A)+P(B)
Mutually Exclusive
The probability that the same number
appears on exactly two of the three dice when three dice are thrown.
5/12 or about 0.4167
The probability of an event occurring is 0.3. If the event is repeated 3 times independently, this is the probability that the event occurs exactly twice.
0.441
Claims filed under auto insurance policies follow a normal distribution with a mean of 19,400 and a standard deviation of 5,000. This is the probability that the average of 25 randomly selected claims exceeds 20,000.
0.2743
You want to receive $5,000 in 3 years, and the interest is compounded annually at an effective annual rate of 6%. This is the amount you need to invest today to achieve that future value.
$4198.10
This expression is equal to
P((A\cup B)^C)
P(A^C \cap B^C)
The probability that a visit to a primary care physician results in neither lab work nor a referral is 35%. If 30% of patients are referred to specialists and 40% require lab work, this is the probability that a visit results in both lab work and a referral.
0.05
An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The benefit decreases by 1000 each successive year until it reaches 0. If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.4. This is the expected benefit under this policy.
2694.40
The waiting times for the first claims from a good driver and a bad driver are independent and exponentially distributed, with means of 6 years and 3 years respectively. This is the probability that the good driver files a claim within 3 years and the bad driver within 2 years.
0.1915
What is the present value of $5,000 due in ten years, assuming money grows according to compound interest with an annual effective rate of 4% for the first three years, 5% for the next two years, and 5.5% for the final five years?
$3084.81