7. When two dice are tossed, let the random variable X represent the minimum value of the two dice and let the random variable Y represent the absolute value of the difference of the two dice. (a) (b) Find the joint probability function. ]Find the marginal probability density function of X and Y, and determine whether X and Y are independent random variables.
7. When two dice are tossed, let the random variable X represent the minimum value of the two dice and let the random variable Y represent the absolute value of the difference of the two dice. (a) (b) Find the joint probability function. ]Find the marginal probability density function of X and Y, and determine whether X and Y are independent random variables.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Need help with this probability question please
Question #7
![1. (a)
When five dice are rolled, what is the probability that at least 4 "ones" come up?
(b)
1
When five dice are rolled, what is the probability of getting a full-house?
(ex: aaabb)
2. In a box, there are 3 fair coins, 2 special coins with heads on both sides and 5 special coins
with tails on both sides. A coin is randomly selected and flipped.
(a)
] If a head comes up, what is the probability that the selected coin is a special
coin with heads on both sides?
(b) [
3. Consider a standard deck of 52 cards. Five cards are randomly drawn by each of three
players.
(a)r
(b)
When the same coin is flipped again, if a head still comes up, what is the
probability that the selected coin is a special coin with heads on both sides?
4. In an office, assume the number of arriving telephone calls has a Poisson distribution with an
average rate of 10 calls per hour.
(a) [
(b) [
(a)
(b)
What is the probability that at least one player receives at least one spade?
What is the probability that at least one player receives 5 spades?
5. In a country, citizens' annual incomes are normally distributed with a mean of $20,000 and a
standard deviation of $4,000.
(a)
(b)
What is the probability that exactly 5 calls arrive in a given 40 minutes?
Assume the office opens at 9:00AM. What is the probability that the first call
arrives between 9:05AM and 9:15AM?
(a)
(b)
] When a citizen is randomly surveyed, what is the probability that his annual
income is below $17,000?
6. Let X be the continuous random variable with the probability density function
f(x) = {(2x+5)/44 if1 ≤x≤5
otherwise
] When 10 citizens are randomly surveyed, what is the probability that their
average annual incomes are below $17,000?
7. When two dice are tossed, let the random variable X represent the minimum value of the two
dice and let the random variable Y represent the absolute value of the difference of the two
dice.
Find E(X) and Var (X).
]Find the cumulative distribution function of X.
Find the joint probability function.
] Find the marginal probability density function of X and Y, and determine
whether X and Y are independent random variables.
15 gram.
(a)
8. In a supermarket, the weight of apples has an approximately normal distribution with the
mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an
approximately normal distribution with the mean of 210 gram and the standard deviation of
When an apple and a pear are randomly selected, what is the probability that
the apple weights more than the pear?
(b) L
If Tom randomly buys 30 apples and 20 pears, what is the probability that their
total weight exceeds 10kg (10kg = 10, 000g)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33eba9e5-eb7d-44a1-93e3-ed0ee897e17f%2F2f530908-abc0-42de-adf5-065029056faf%2Fts53rt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (a)
When five dice are rolled, what is the probability that at least 4 "ones" come up?
(b)
1
When five dice are rolled, what is the probability of getting a full-house?
(ex: aaabb)
2. In a box, there are 3 fair coins, 2 special coins with heads on both sides and 5 special coins
with tails on both sides. A coin is randomly selected and flipped.
(a)
] If a head comes up, what is the probability that the selected coin is a special
coin with heads on both sides?
(b) [
3. Consider a standard deck of 52 cards. Five cards are randomly drawn by each of three
players.
(a)r
(b)
When the same coin is flipped again, if a head still comes up, what is the
probability that the selected coin is a special coin with heads on both sides?
4. In an office, assume the number of arriving telephone calls has a Poisson distribution with an
average rate of 10 calls per hour.
(a) [
(b) [
(a)
(b)
What is the probability that at least one player receives at least one spade?
What is the probability that at least one player receives 5 spades?
5. In a country, citizens' annual incomes are normally distributed with a mean of $20,000 and a
standard deviation of $4,000.
(a)
(b)
What is the probability that exactly 5 calls arrive in a given 40 minutes?
Assume the office opens at 9:00AM. What is the probability that the first call
arrives between 9:05AM and 9:15AM?
(a)
(b)
] When a citizen is randomly surveyed, what is the probability that his annual
income is below $17,000?
6. Let X be the continuous random variable with the probability density function
f(x) = {(2x+5)/44 if1 ≤x≤5
otherwise
] When 10 citizens are randomly surveyed, what is the probability that their
average annual incomes are below $17,000?
7. When two dice are tossed, let the random variable X represent the minimum value of the two
dice and let the random variable Y represent the absolute value of the difference of the two
dice.
Find E(X) and Var (X).
]Find the cumulative distribution function of X.
Find the joint probability function.
] Find the marginal probability density function of X and Y, and determine
whether X and Y are independent random variables.
15 gram.
(a)
8. In a supermarket, the weight of apples has an approximately normal distribution with the
mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an
approximately normal distribution with the mean of 210 gram and the standard deviation of
When an apple and a pear are randomly selected, what is the probability that
the apple weights more than the pear?
(b) L
If Tom randomly buys 30 apples and 20 pears, what is the probability that their
total weight exceeds 10kg (10kg = 10, 000g)?
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