JCS me la W Of large numbers tell you about the results you are likely to get? noon and 1:00 every day, 14. Speedy Driver. Suppose a person who has a habit of driving fast has never had a traffic citation. What does it mean to say that "the law of averages [large numbers] will catch up with him"? Is it true? Explain. a. What is the probabilit between noon and 12:20 that case? (Exercise 21 b. What is the probabili between 12:20 and 1:00 15-18: Expected Value in Games. Find the expected value (to you) of the described game. Would you expect to win or lose money in 1 that case? game? In 100 games? Explain. c. Overall, what is you 15. You are given 6 to 1 odds against tossing three heads with three coins, meaning you win $6 if you succeed and $1 if you fail. d. Would your expecte the bus arrived at equ you lose 1:00)? Explain. 16. You are given 9 to 1 odds against tossing three heads with three coins, meaning you win $9 if you succeed and you lose $1 if you fail. 23. Gambler's Fallacy an game in which you w tail appears. In the fi times and tails come 17. You are given 2 to 1 odds against rolling two even numbers with the roll of two fair dice, meaning you win $2 if you succeed and lose $1 if you fail. a. What percentage 100 tosses? What is you 18. You are given 7 to 1 odds against rolling a double number (for example, two 1s or two 2s) with the roll of two fair dice, meaning you win $7 if you succeed and you lose $1 if you fail. b. Suppose you toss tosses), and at that Is this increase in law of large numb at this point? 19-20: Insurance Claims. Find the expected value (to the company) per policy sold. If the company sells 10,000 policies, what is the expected profit or loss? Explain. c. How many hea order to break ev for $1000, Based on past data,
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Question. 18
![JCS me la W Of large
numbers tell you about the results you are likely to get?
noon and 1:00 every day,
14. Speedy Driver. Suppose a person who has a habit of driving
fast has never had a traffic citation. What does it mean to say
that "the law of averages [large numbers] will catch up with
him"? Is it true? Explain.
a. What is the probabilit
between noon and 12:20
that case? (Exercise 21
b. What is the probabili
between 12:20 and 1:00
15-18: Expected Value in Games. Find the expected value (to you)
of the described game. Would you expect to win or lose money in 1
that case?
game? In 100 games? Explain.
c. Overall, what is you
15. You are given 6 to 1 odds against tossing three heads with
three coins, meaning you win $6 if you succeed and
$1 if you fail.
d. Would your expecte
the bus arrived at equ
you
lose
1:00)? Explain.
16. You are given 9 to 1 odds against tossing three heads with
three coins, meaning you win $9 if you succeed and you lose
$1 if you fail.
23. Gambler's Fallacy an
game in which you w
tail
appears. In the fi
times and tails come
17. You are given 2 to 1 odds against rolling two even numbers
with the roll of two fair dice, meaning you win $2 if you
succeed and lose $1 if you fail.
a. What percentage
100 tosses? What is
you
18. You are given 7 to 1 odds against rolling a double number
(for example, two 1s or two 2s) with the roll of two fair dice,
meaning you win $7 if you succeed and you lose $1 if you fail.
b. Suppose you toss
tosses), and at that
Is this increase in
law of large numb
at this point?
19-20: Insurance Claims. Find the expected value (to the company)
per policy sold. If the company sells 10,000 policies, what is the
expected profit or loss? Explain.
c. How many hea
order to break ev
for
$1000, Based on past data,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80110b79-5e7a-40a6-a76b-a801605b026f%2Fd6c4073c-8b02-48e4-a404-60509c1e9b06%2Fyoyi1fq.jpeg&w=3840&q=75)
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