3. A box contains 5 red balls, 3 blue balls and 1 black balls.
Take two...
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).A box contains 20 balls. Five are blue, seven are red, and
eight are black. Four balls are selected at random and with
replacement. Calculate the probability that fewer than two red
balls are chosen.
ANSWER: .5630
2. A company recently hired 50 employees. You are given:
(a) Thirty employees are from Iowa; the remaining came from
New York.
(b) Of the employees who are from Iowa, 30% are males and the
remaining are females.
(c) Of the employees who...
Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box
2 contains 5 red balls, 3 green balls and 1 white ball. One ball of
unknown color is transferred from Box 1 to Box 2. (a) What is the
probability that a ball drawn at random from Box 2 is green? (b)
What is the probability that a ball drawn from Box 1 is not
white?
1) An urn contains 10 balls, 2 red, 5 blue, and 3 green balls.
Take out 3 balls at a random, without replacement. You win $2 for
each green ball you select and lose $3 for each red ball you
select. Let the random variable X denote the amount you win,
determine the probability mass function of X.
2) Each of the 60 students in a class belongs to exactly one of
the three groups A,B, or C. The membership...
In a box of 5 balls, 2 are red and 3 are blue. Two
balls are randomly selected (without replacement). Let X be the
number of red balls in the two selected balls.
a. Find the probability distribution of X (i.e., list
all possible values of X and their corresponding
probabilities).
b. Find the expected value and the standard deviation
of X.
An urn contains 5 red balls and 5 blue balls.
(a) If 3 balls are selected all at once, what is the
probability that 2 are blue and 1 is red?
(b) If 3 balls are selected by pulling out a ball, noting its
color, and putting it back in the urn before the next section,
what is the probability that only the first and third balls drawn
are blue?
(c) If 3 balls are selected one at a...
An urn contains 7 black balls, 4 red balls, 3 white balls and 1
blue ball, and a player is to draw one ball. If it is black, he
wins $1, if it is red, he wins $2, if it is white he wins $3 and if
it is blue, he pay $25.
a. Set up the empirical probability distribution for the random
variable X, the payoff of the game.
Game Payoff (X)
Probability [P(X)
$1
$2
$3
$4
b....
Box A contains 6 red balls and 3 green balls, whereas box B
contains 3 red ball and 15 green balls.
Stage one. One box is selected at random in such a way that box
A is selected with probability 1/5 and box B is selected with
probability 4/5.
Stage two. Finally, suppose that two balls are selected at
random with replacement from the box selected at stage one.
g) What is the probability that both balls are red?
h)...
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 box contains 8 red balls, 4 green balls, and 3 blue balls. You
pull 2 balls from the box (one at a time) WITHOUT
replacement.
**LEAVE ALL ANSWERS AS FRACTIONS**
Find the probability of the following:
a.) P(Red on 1st ball AND Red on 2nd ball) =
b.) P(Green on 1st ball AND Red on 2nd ball)
=
c.) P(Blue on 1st ball AND Green on 2nd ball)
=
d.) What is the probability of drawing 2 green
balls...
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