Can you help me understand how to solve this problem? (I need the process and math behind it, not just the answer).
Suppose I have a 10-sided die. It's clear enough that the odds of rolling a 1 are 10% for any single roll. What, then, is the likelihood that I will roll a 1 given 10 rolls? Given 5 or 20 rolls?
I'd need to solve this for any single-event probability, too -- not just for a 10-sided die.

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Solution. We first consider a 10-sided die. Then we can generalize this idea to any m-sided die. Obviously, if we roll a 10-sided die, we get 1 with probability p=10%.
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<br>(1) If we roll this die 10 times, then denote the number that we get 1 by X. We know that X is a random variable which ...

Solution Summary

Can you help me understand how to solve this problem? (I need the process and math behind it, not just the answer).
Suppose I have a 10-sided die. It's clear enough that the odds of rolling a 1 are 10% for any single roll. What, then, is the likelihood that I will roll a 1 given 10 rolls? Given 5 or 20 rolls?
I'd need to solve this for any single-event probability, too -- not just for a 10-sided die.

Let A and B be events, both having positive probability.
Show that if P(A|B) > P(A), then P(B|A) > P(B).
We know the following definitions:
Conditional Probability:
The probability of event B given event A is P(B|A)=P(AandB)/P(A)
The probability of event A given event B is P(A|B)=P(Aand B)/P(B)
Independent Events:
T

Outcomes and event probability
Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The outcomes are listed in the table below. Note that each outcom

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What is the probability that event A happens?

The probability distribution for the random variable x is as follows
x is 20 25 30 35
f(x) is .20 .15 .25 .40
a. Is this probability distribution valid? Explain.
b. What is the probability that x=30?
c. What is the probability that x is less than or equal to 25?
d. What is the probability that x is greater than 30?

Urn I contains five red chips and four white chips; urn II contains four red and five white chips. Two chips are drawn cimultaneously from urn I and placed in urn II. Then a single chip is drawn from urn II. What is the probability that the chip drawn from urn II is white?

If a die rolled one time, classical probability would indicate that the probability of a "two" should be 1/6. If the die is rolled 60 times and comes up "two" only 9 times, does this suggest that the die is "loaded"? Why or why not?
It is reported that about 35% of adults attend sports event during the previous year. W

A single die is rolled once. You lose $12 if a number divisible by 3 turns up. How much should you win if a number not divisible by 3 turns up for the game to be fair?
How would I set this up, and what formulas?