Question

There are 5 red, 4 blue, 6 green and 3 black balls in a box. Ahmed
draws 5 balls from the box at random. What is the probability that
at least three of them are blue?

Answer #1

TOPIC:Hypergeometric distribution.

A box contains 6 red balls and 4 blue balls. Drawing three balls
from the box randomly, what is the probability that exactly two of
the balls are red?

In a box are 3 red balls and 5 blue balls. From this box are
drawn 4 balls and placed in a second box. Given the ball drawn from
the second box is red, what is the probability that 2 red and 2
blue balls were transferred from box 1 to box 2?

A box contains 5 blue, 10 green, and 5 red chips. We draw 4
chips at random and without replacement. If exactly one of them is
blue, what is the probability mass function of the number of green
balls drawn?

Box I contains 7 red and 3 black balls; Box II contains 4 red
and 5 black balls. After a randomly selected ball is transferred
from Box I to Box II, 2 balls are drawn from Box II without
replacement. Given that the two balls are red, what is the
probability a black ball was transferred?

Suppose you have a box with 10 red balls, 4 green balls, and 6
blue balls. Answer the following questions. Think about the
questions below. They look similar, but how are they different?
a) You randomly select two balls from the box. What is the
probability of selecting two red balls?
b) Suppose you are asked to draw a ball, return whatever you
picked, and draw another ball. This is called sampling with
replacement. What is the probability of selecting...

Select 5 marbles at random from a jar with 8-red,
3-blue,2-purple, 3-black and 4- green.
What is probability that all are blue marbles?
What is probability of selecting 2-blue and 3-red marble?
What is probability of selecting one of each color?
What is probability of selecting at least 2 green marbles?

For this problem, assume the box contains 8 blue balls, 5 red
balls, and 4 white balls, and that we choose two balls at random
from the box.
What is the probability of neither being blue given that neither
is red?

Box 1 contains 4 red balls, 5 green balls and 1 yellow ball.
Box 2 contains 3 red balls, 5 green balls and 2 yellow
balls.
Box 3 contains 2 red balls, 5 green balls and 3 yellow
balls.
Box 4 contains 1 red ball, 5 green balls and 4 yellow balls.
Which of the following variables have a binomial
distribution?
(I) Randomly select three balls from Box 1 with replacement. X =
number of red balls selected
(II) Randomly...

Exercise 2 A box contains 3 white balls, 4 red balls and 5 black
balls. A ball is picked, its color recorded and returned to the
box(with replacement). Another ball is then selected and its color
recorded.
1. Find the probability that 2 black balls are selected.
2. Find the probability that 2 balls of the same color are
selected.
Now 4 balls are picked with replacement
3.Find the probability no red balls are selected.
4.Find the probability that the...

An urn contains 1 white, 2 black, 3 red, and 4 green balls. If 6
balls are selected randomly (without replacement) and X represents
the number of selections that are either red or green, find: (a)
the probability mass function for X. (b) the expected value of X
(calculate this value directly by using the probability mass
function from part a).

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