A bag contains two orange and six black balls. You take two
balls from the bag,...
A bag contains two orange and six black balls. You take two
balls from the bag, one by one, with replacement. How many orange
balls do you expect to get?
An urn contains six white balls and four black balls. Two balls
are randomly selected from the urn. Let X represent the
number of black balls selected.
(a) Identify the probability distribution of X. State
the values of the parameters corresponding to this
distribution.
(b) Compute P(X = 0), P(X =
1), and P(X = 2).
(c) Consider a game of chance where you randomly select two
balls from the urn. You then win $2 for every black ball selected...
3. A box contains 5 red balls, 3 blue balls and 1 black balls.
Take two balls out randomly. Let X be number of red balls and Y be
the number of black balls.
(1) Find the joint distribution of (X, Y ).
(2) Find P(X = 1|Y = 1).
Urn A contains four white balls and three black balls. Urn B
contains six white balls and seven black balls. A ball is drawn
from Urn A and then transferred to Urn B. A ball is then drawn from
Urn B. What is the probability that the transferred ball was white
given that the second ball drawn was white? (Round your answer to
three decimal places.)
I can't seem to figure this out! Please help! Thank you!
A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red
Suppose that we have two bags each containing black and white
balls. One bag contains two times as many white balls as black
balls. The other bag contains two times as many black balls as
white. Suppose we choose one of these bags at random. For this bag
we select five balls at random, replacing each ball after it has
been selected. The result is that we find all balls are white
balls. What is the probability that we were...
Bag 1 contains 3 red balls and 7 green balls. Bag 2 contains 8
red balls and 4 green balls. Bag 3 contains 5 red balls and 11
green balls. Bag 1 is chosen twice as often as either Bag 2 or Bag
3 (which have the same probability of being chosen). After a bag is
chosen, a ball is chosen at random from that bag. Calculate the
probability that:
a) a red ball is chosen
b) a red ball...
Suppose there are three balls in a bag. One ball is black and
two others are white. Three people, A, B and C, will pick a ball in
this order. Instead of deciding the winner by the first black ball,
the person who picks the black ball for the second time will be the
winner. For example, if A picks the black ball for his first pick,
A is not the winner. He just returns it to the bag. And...
A box contains three white balls, two black balls, and one red
ball. Three balls are drawn at random without replacement. Let Y1
be the number of white balls drawn, and Y2 the number of black
balls drawn. Find the distribution of Z = Y1 × Y2
A bag contains four balls labelled 0,1,2 and 3. Two balls are
chosen at random, one after the other and without replacement. Let
X be the label on the first one and Y be the label on the second
ball.
1. Find joint probability mass function of X and Y?
2. Calculate E(x), E(Y) , E(XY), and Cov (XY)?
Please explain answer.
An urn contains 5 red, 3 orange, and 2 blue balls. Two balls are
randomly selected simultaneously.
(a) What is the sample space?
(b) Define an RV X as the number of orange balls selected. Show
the map from the sample space to X.
(c) Find the PMF of X.
(d) Find the CDF of X.
i have the solutions can one show how to find the probablity on
4c