there is a bag containing 2 red balls, 2 blue balls, 2 brown
balls, and 2...
there is a bag containing 2 red balls, 2 blue balls, 2 brown
balls, and 2 green balls. A subset of 4 balls are randomly drawn.
Consider that X is the number of colors drawn in this subset, what
is E(X)?
Assume that a bag initially contains 6 balls: 2 red, 2 green and
2 blue balls. At each step, you choose a ball from the bag at
random, note its color, but do not put it back into the bag.
Instead, you add to the bag two balls, which are of of two
different colors, and different in color from the color of the
removed ball. (For example, if you choose a red ball in the first
step, then after...
We have a bag that contains n red balls and n blue balls. At
each of 2n rounds we remove one of the balls from the bag randomly,
and place it in one of available n bins. At each round, each one of
the balls that remain in the bag is equally likely to be picked, as
is each of the bins, independent of the results of previous rounds.
Let Nk be the number of balls in the k-th bin...
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...
Consider an urn containing 3 red balls, 5 yellow balls, 7 blue
balls, and 6 violet balls. If 4 balls are drawn at random, what is
the probability of drawing one of each color?
Suppose we draw 8 balls from the urn above. What is the
conditional probability that 4 of them are blue with respect to the
event that none of them are yellow?
Two
balls are drawn, without replacement, from a bag containing 11 red
balls numbered 1-11 and 5 white balls numbered 12-16. (Enter your
probabilities as fractions)
(a) What is the probability that the second ball is red, given
that the first ball is white?
(b) What is the probability that both balls are even
numbered?
(c) What is the probability that the first ball is red and
even-numbered and the second ball is even numbered?
Question 10
:A jar contains 2 red balls, 2 blue balls, 2 green balls, and
3orange balls. Balls are randomly selected, without
replacement,until 2 of the same colour are obtained. Calculate the
probability thatmore than 3 balls must be selected
Suppose you have a bag containing 2 red marbles, 3 white
marbles, and 4 blue marbles.
a) if you draw 3 marbles simultaneously, what is the probability
that you get one of each color?
b) If you draw 3 marbles one at a time, what Is the probability
that you get one of each color?
A bag contains 4 Blue, 5 red and 3 green balls. Debolina is
asked to pick up three balls at random, one by one without
replacement from that bag. If the balls picked up are of same
colour then Debolina will get Rs. 7000, if the balls picked up are
of different colour, then she will get Rs. 9000, but otherwise she
has to pay Rs. 4000.
a) Find the expected gain of Debolina if she plays the game.
b)...
There are 10 identical red balls, 10 identical blue
balls, 10 identical green balls and 2 distinct boxes. How many ways
to place all the 30 balls in the two boxes such that each box
contains 15 balls?
Two golf balls are selected with replacement from a bowl
containing 7 red and 3 blue balls
What is the probability that both balls are red?
What is the probability that both balls are blue?
What is the probability that the first ball is red and the
second ball is blue?
What is the probability that the first ball is blue and the
second ball is red?
What is the probability that the two balls selected are the
same color?...