Question

Suppose that balls are successively distributed among 8 urns, with each ball being equally likely to be put in any of these urns. What is the probability that there will be exactly 4 nonempty urns after 9 balls have been distributed?

Answer #1

Three balls are randomly dropped into three boxes. Assume that
any ball is equally likely to fall into each box. Specify an
appropriate sample space and determine the probability that exactly
one box will be empty.

A magic bag contains infinitely many balls labeled 1 to n with
each ball being equally likely to be drawn from the bag. There are
also n boxes labeled 1 to n. Suppose you fill the boxes by choosing
a random ball from the magic bag. A match occurs when the
ball labeled i is placed in the box labeled i. For an arbitrary k
in {0,1,...,n} what is the probability that you have k matches?
What is the probability...

You play the following game against your friend. You have 2 urns
and 4 balls One of the balls is black and the other 3 are white.
You can place the balls in the urns any way that you'd like,
including leaving an urn empty. Your friend will choose one urn at
random and then draw a ball from that urn. ( If he chooses an empty
urn, he draws nothing.) She wins if she draws the black ball and...

In the pool, there are 8 white balls numbered 1 to 8 and 4 black
balls numbered 1 to 4. We draw 3 balls without returning them to
the pool. What is the probability that: (a) there is (exactly) 1
black ball among the drawn balls? (b) all drawn balls have even
numbers?

Suppose 5 distinct balls are distributed into 3 distinct boxes
such that each of the 5 balls can get into any of the 3 boxes.
1) What is the Probability that box 1 has exactly two balls and
the remaining balls are in the other two boxes.
2) What is the probability that there is exactly one empty
box?

Suppose that an urn contains 8 red balls and 4
white balls. We draw 2 balls
from the urn without replacement.
Now suppose that the balls have
different weights, with each red ball having weight
r and each white ball having weight w. Suppose that the
probability that a given ball in
the urn is the next one selected is its weight divided by the
sum of the weights of all
balls currently in the urn.
Now what is the...

Suppose you have a big vat of balls and that 60% of the balls
are green and 40% of the balls are red. Suppose you randomly select
a ball, record the color, then put the ball back, and repeat the
process.
a) What is the probability that the first red ball you encounter
will be the sixth ball you pull from the vat? Clearly state which
probability distribution’s PMF you are using to perform this
calculation as well as which...

9 different balls are distributed to 4 different boxes, where
each box can contain at most one ball. Empty boxes are allowed,
that it is possible that only one box has one ball, but the other
boxes don’t have any balls. Find the possible number of ways for
the distribution.

1. SAMPLING WITHOUT REPLACEMENT
a. A bin contains 4 red balls and 8
blue balls. Several balls are drawn from the bin. What is the
probability that the 6th ball and the 8th ball drawn are both
red?
b. A bin contains 5 red balls and 9 blue balls. Several
balls are drawn from the bin. Given that the 4th ball drawn is
blue, what is the probability that the 8th ball drawn is
red?
c. A bin contains 5...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 21 minutes ago

asked 23 minutes ago

asked 23 minutes ago

asked 47 minutes ago

asked 47 minutes ago

asked 47 minutes ago

asked 51 minutes ago

asked 58 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago