Question
In: Math
A box contains 7 black balls and a single red ball. Peter and Frances draw without...
A
box contains 7 black balls and a single red ball. Peter and Frances
draw without replacement balls from this urn, alternating after
each draw until the red ball is drawn. The game is won by the
player who happens to draw the single red ball. Peter is a
gentleman and offers Frances the choice of whether she wants to
start or not. Frances has a hunch that she might be better off if
she starts; after all, she might succeed in the first draw. On the
other hand, if her first draw yields a black ball, then Peter’s
chances to draw the red ball in his first draw are increased,
because then one black ball is already removed from the urn. How
should Frances decide in order to maximize her probability of
winning?
Solutions
milcah answered 9 months agoRelated Solutions
A box contains three white balls, two black balls, and one red ball. Three balls are...
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
An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball,...
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....
a box contains two red balls , one white ball and one blue ball. A sample...
a box contains two red balls , one white ball and one blue ball.
A sample of two balls was drawn randomly, respectively (without
return), If the variable X express the number of white balls and
the variable Y express the number of blue balls in the sample, find
:
A- Fxy(0,1)
B- Coefficient of correlation between the two variables and then
commented on it
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) Find the joint distribution of (X, Y ).
(2) Find P(X = 1|Y = 1).
Box A contains 6 red balls and 3 green balls, whereas box B contains 3 red...
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)...
Following are three boxes containing balls. Box #1 contains 2 black balls and 1 white ball....
Following are three boxes containing balls. Box #1 contains 2
black balls and 1 white ball. Box #2 contains 2 black balls and 2
white balls. Box #3 contains 1 black ball and 2 white ball. Draw a
ball from Box 1 and place it in Box 2. Then draw a ball from Box 2
and place it in Box 3. Finally draw a ball from Box 3 . What is the
possibility that the last ball drawn, from Box...
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls. Box B...
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls.
Box B conatins 2 yellow balls and 2 red balls. Box C contains 2
yellow balls and 1 red ball. First, we randomly choose between Box
A and Box B. Then we randomly choose a ball from the selected box
and put the ball into Box C. Lastly, we randomly choose a ball from
Box C.
Let E1 be the event that Box A is chosen...
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls. Box B...
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls.
Box B contains 2 yellow balls and 2 red balls. Box C contains 2
yellow balls and 1 red ball. First, we randomly choose between Box
A and Box B. Then we randomly choose a ball from the selected box
and put the ball into Box C. Lastly, we randomly choose a ball from
Box C.
Let E1 be the event that Box A is chosen...
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls. Box B...
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls.
Box B conatins 2 yellow balls and 2 red balls. Box C contains 2
yellow balls and 1 red ball. First, we randomly choose between Box
A and Box B. Then we randomly choose a ball from the selected box
and put the ball into Box C. Lastly, we randomly choose a ball from
Box C.
Let E1 be the event that Box A is chosen...
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls. Box B...
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls.
Box B conatins 2 yellow balls and 2 red balls. Box C contains 2
yellow balls and 1 red ball. First, we randomly choose between Box
A and Box B. Then we randomly choose a ball from the selected box
and put the ball into Box C. Lastly, we randomly choose a ball from
Box C.
Let E1 be the event that Box A is chosen...
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