Question

**A fair die is rolled once. Let A = the die shows an odd
number. Let B = the die shows a number**

**greater than 4.**

**(a) Find A ∪ B.**

**(b) Find A ∩ B.**

**(c) Find P(A ∪ B)**

Answer #1

This is the solution for given problem..

Two identical fair 6-sided dice are rolled
simultaneously. Each die that shows a number less than or equal to
4 is rolled once again. Let X be the number of dice that show a
number less than or equal to 4 on the first roll, and let Y be the
total number of dice that show a number greater than 4 at the
end.
(a) Find the joint PMF of X and Y . (Show your final
answer in a...

A fair die is rolled. Find the probability of rolling
a. a 4
b. a 5
c. a number less than 5
d. a number greater than 4
e. a number less than 20
f. a number greater than 17
g. an odd number
h. a 4 or a 5
i. a 4 or an even number
j. a 4 and a 5
k. a 4 and an even number
l. a 4 or an odd

A fair die is rolled repeatedly. Let X be the random variable
for the number of times a fair die is rolled before a six appears.
Find E[X].

A fair die is rolled 1000 times. Let A be the event that the
number of 6’s is in the interval[150,200], and B the event that the
number of 5’s is exactly 200. (a) Approximate P(A).(b) Approximate
P(A|B).

Bill pays $1 for the privilege of rolling a fair die. If an odd
number shows up, Bill will win as many dollars as the number that
shows up on the die. If an even number shows up, he will lose $3.
Find the following:
a) The probability function of Bill’s net winnings.
b) Bill’s expected net winnings and the standard deviation of
these winnings.

A fair die is successively rolled. Let X and Y denote,
respectively, the number of rolls necessary to obtain a 5 and a 4.
Find (a) EX, (b) E[X|Y =1] and (c) E[X|Y=4].

A fair die is successively rolled. Let X and Y denote,
respectively, the number of rolls necessary to obtain a 5 and a 4.
Find (a) E X, (b) E[X|Y = 1] and (c) E[X|Y = 4].

a fair die was rolled repeatedly.
a) Let X denote the number of rolls until you get at least 3
different results. Find E(X) without calculating the distribution
of X.
b) Let S denote the number of rolls until you get a repeated
result. Find E(S).

Two fair six-sided dice are rolled once. Let (X, Y) denote the
pair of outcomes of the two rolls.
a) Find the probability that the two rolls result in the same
outcomes.
b) Find the probability that the face of at least one of the
dice is 4.
c) Find the probability that the sum of the dice is greater than
6.
d) Given that X less than or equal to 4 find the probability
that Y > X.

Alice rolled a fair, six-sided die ten times and counted that
she got an even number six times.
Which of the following statements is FALSE?
The distribution of the count of getting an
odd number is binomial.
The distribution of the count of getting an
even number is binomial.
The distribution of the count of getting an
even number cannot be modeled as approximately normal if the die is
rolled more than 100 times.
The distribution...

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