Probability Examples and Explanations

Income percentile ranks are numbers from 0 to 100 that indicate where you sit in the income distribution - for example, 75 would mean you earn more income than three quarters of people, but less than the top quarter. Let's assume a child's expected income percentile is a linear function of their parents' income percentile. It turns out the intercept is enough to pin down the slope. Do you see why? If the intercept is 20 - which means the lowest-income parents have children who end up at the 20th percentile, on average - what is the slope?
This problem is from an app called probability puzzles.
My approach: I realised $y=ax+b$ could be the line for child but we don't have any information about the slope. We know that percentile is uniformly distributed between 0 and 100 so expected value is 50 but I don't see how to proceed from here.

The standard telephone number in the US has 10 digits: for example, NOVA's telephone number is (703) 323-3000, How many phone numbers are possible for the 703 area code it the first digit that follows the 703 cannot be a or a 1?

Classify the following as an example of classical probability, empirical probability or subjective probability. Based on a sample of 200 cats, the probability that a randomly chosen cat has blue eyes is 0.76
a) empirical probability
b) subjective probability
c) classical probability

The area code of a telephone number consists of 3 numbers (for example, 571). How many different area codes are possible?
1,000,000
Correct Answer
Not Provided
1.000
10,000

A machine fills containers with a particular product. The standard deviation of filling weights is known from past data to be 0.6 ounce. If only $2\mathrm{\%<!--\; \%\; -->}$ of the containers hold less than 18 ounces, what is the mean filling weight for the machine? That is what must $\mathrm{\mu <!--\; \mu \; -->}$ equal? Assume the filling weights have a normal distribution.

Suppose you purchase one California SuperLotto Plus lottery ticket. Here's how to play: Pick five numbers from 1 to 47 (no repeats allowed) and then pick one Mega number from 1 to 27.
a. Find the probability you get the Mega number, but none of your five numbers match the winning numbers.
b. Find the probability you get the Mega number and exactly two of your five numbers match the winning numbers.
c. Find the probability you get the Mega number and all give of your five numbers match the winning numbers.

What is the probability of obtaining ten tails in a row when flipping a coin? Interpret this probability. The probability of obtaining ten tails in a row when flipping a coin is

For a binomial distribution, which probability is not equal to the probability of 1 success in 5 trials where the probability of success is 0.4?
the probability of 4 failures in 5 trials where the probability of success is 0.6
the probability of 1 success in 5 trials where the probability of failure is 0.6
the probability of 4 failures in 5 trials where the probability of failure is 0.6
the probability of 4 failures in 5 trials where the probability of success is 0.4

The probability of 6 while roling a dice equal to $\frac{1}{6}$ is an example of
objective probability
axiomatic probability
conditional probability
subjective probability
classic or symmetric probability

For the Illinois Lottery's PICK 3 game, a player must match a sequence of three repeatable numbers, ranging from 0 to 9, in exact order (for example 5-5-2.) With a single ticket, what is the probability of matching the three winning numbers?

In a random experiment, two dice are thrown. Find the probability that the sum of the rolled points is 8. Round the result to the nearest thousandth.

Complete the following probability table. (Round Prior Probabilty and Posterior Probability answer to 2 decimal places and Joint Probability answer to 4 decimal places)
$\begin{array}{|cccc|}\hline \text{Prior Probability}& \text{Conditional Probability}& \text{Join Probability}& \text{Posterior Probability}\\ P(B)0.52& P(A|B)0.13& P(A\cap <!--\; \cap \; -->B)& P(B|A)\\ P(B^C)& P(A|B^C)0.47& P(A\cap <!--\; \cap \; -->S^C)& P(B^C|A)\\ \text{Total}& & P(A)& \text{Total}\\ \hline\end{array}$

At the ceramic tableware factory, 10% of the produced plates are defective. During product quality control, 75% of defective plates are detected. The rest of the plates are for sale. Find the probability that a plate randomly selected at the time of purchase has no defects. . Round your answer to the nearest hundredth.

A die is thrown twice. Find the probability that a number greater than 3 is rolled both times.

In a family with 12 children the p = probability of a boy = 0.5. Find the binomial exact probability of less than 1 boy. And find the normal approximate probability of less then 1 boy.
a) Exact probability = 0.011, Approx probability = 0.013
b) Exact probability = 0.019, Approx probability = 0.022
c) Exact probability = 0.003, Approx probability = 0.005
d) Exact probability = 0.055, Approx probability = 0.057

Classify the statement as an example of classical probability, emprical probability, or subjective probability. Explan your reasoning. The probability of winning a 500 - ticket reffle with 10 tickets is $\frac{10}{500}=0.02$
a) Empirical probability because the probability results from an estimate
b) Classical probability because each outcome in the sample space is equally likely
c) Subjective probability because the probability results from an estimete
d) Classical probability because the probability is based on observations obtained from a probability experiment
e) Subjective probability because each outcome in the sample space is equally likely
f) Empirical probability because the probability is based on observations obtained from a probability experiment

"Draw one card from a standard deck of playing cards. Let’s examine the independence of 3 events ‘the card is an ace’, ‘the card is a heart’ and ‘the card is red’. Define the events as $A{=}^{\prime }ac{e}^{\prime }$, $H=‘heart{s}^{\prime }$, $R=‘re{d}^{\prime }$."
With $P(A)=\frac{1}{13},P(H)=\frac{1}{4}$ and $P(R)=\frac{1}{21}$ I get $\frac{1}{4}$ for $P(H|R)$. So this basically says that P(H) and P(R) are independent, since H and P are independent iff $P(H|R)=P(H)$ . I know that that's not correct from the source, so now I am wondering how I can then calculate the conditional probability for dependent events and how I would know beforehand. Why is $P(H|R)$ actually $\frac{1}{2}$ ?