Question

An urn has 12 balls. 8 are white balls and 4 are black balls.

If we draw a sample of 3 balls (i.e., picking without replacement) and given that the first two balls selected were a black ball and a white ball, what is the conditional probability of the third ball drawn being white?

Answer #1

let drawing of white and black ball is represented by W and B

P(first two select were black and white)=P(WBW)+P(WBB)+P(BWW)+P(BWB)

=(8/12)*(4/11)*(7/10)+(8/12)*(4/11)*(3/10)+(4/12)*(8/11)*(7/10)+(4/12)*(8/11)*(3/10)

=16/33

P(first two are black and white and third is white)=P(WBW)+P(BWW)

=(8/12)*(4/11)*(7/10)+(4/12)*(8/11)*(7/10)

=56/165

therefore P(third is white given first two are black and white)

=(56/165)/(16/33)=7/10

(Note: this can easily be solved by the fact that after removing 1st two balls one of which is white and other black, there remains 10 balls in which there are 7 whites, therefore probability of white =7/10)

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...

From an urn containing 3 white and 2 black balls, two balls
are drawn one after the other
without replacement. What is the probability that the first
ball drawn is white and the
second black?

An urn contains 12 white and 21 black balls. Balls are
drawn one by one, without replacement, until 4 black balls are
drawn. Find an expression for the probability that the total number
of balls drawn is x.

There are 8 black balls and 7 red balls in an urn. If 4 balls
are drawn without replacement, what is the probability that no more
than 1 black ball is drawn? Express your answer as a fraction or a
decimal number rounded to four decimal places.

An urn contains 12 white and 21 black balls. Balls are
drawn one by one, with replacement, until 4 white balls are drawn.
Find an expression for the probability that the total number of
balls drawn is x.

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?

An urn contains 15 white and 21 black balls. Balls are
drawn one by one, without replacement, until 6 white balls are
drawn. Find an expression for the probability that the total number
of balls drawn is x.

Urn A has 8 Red balls and 5 Green balls while Urn B has 1 Red
ball and 3 Green balls.
A fair die is tossed. If a “5” or a “6” are rolled, a ball is drawn
from Urn A. Otherwise, a ball is drawn from Urn B.
(a) Determine the conditional probability that the chosen ball is
Red given that Urn A is selected?
(b) Determine the conditional probability that the chosen ball is
Red and Urn B...

An urn contains 3 white balls and 7 red balls. A second urn
contains 7 white balls and 3 red balls. An urn is selected, and the
probability of selecting the first urn is 0.2. A ball is drawn from
the selected urn and replaced. Then another ball is drawn and
replaced from the same urn. If both balls are white, what are the
following probabilities? (Round your answers to three decimal
places.)
(a) the probability that the urn selected...

One urn contains 10 red balls and 10 white balls, a second urn
contains 8 red balls and 4 white balls, and a third urn contains 5
red balls and 10 white balls. An urn is selected at random, and a
ball is chosen from the urn. If the chosen ball is white, what is
the probability that it came from the third urn? Justify your
answer.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 18 minutes ago

asked 21 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago