In: Statistics and Probability

Three people are brought into a room. A hat is placed on each person’s head. The hat is equally likely to be Red or Blue. (So each of the 8 possibilities is equally likely.) Each person sees the colors of the other people’s hats, but not their own. Each person, without communication, writes down one of the following: "My hat is red", "My hat is blue" or "Pass". All three people will be put in jail unless (a) at least one of them doesn’t pass, and (b) everyone who doesn’t pass is right about his/her own hat color. Importantly, they can agree ahead of time on a strategy, with the hopes of not going to prison.

(a) What is the probability that they are not sent to prison if each person guesses the color of his/her own hat?

(b) What is the probability that they are not sent to prison if two of them pass and 1 of them guesses?

(c) What is the probability that they are not sent to prison if they use the following strategy: Each person looks at the other two hats. If they are both blue, then the person guesses red. If they are both red, then the person guesses blue. If they are different, the person passes.

If everyone of the three person guesses the color of his hat, It is likely that each person is taking a 50% chance. There are two colors with equally like chance of 1/2 in a guess like tossing a coin with blue and red color on it. There are 8 outcomes, there is chance of 4 will be correct, so 4/8.

Two persons pass, and third guess the color of his hat, he thinks of the possibilities after seeing the colors of the two persons. Since there are two colors Red and Blue, he can reject the two possibilities that is one with all three blue or all three red. Now he can gues one of the six other possibilities of the hat colors, so he has chance of guessing the right color by 6/8 = 0.75=75%.

First two hats of same colors occur in 2 ways, One is Blue-Blue; another one is Red - Red. If one guesses the other color, he can be right, It occurs in 2 cases with a probability 2/8=25%, again this happens one of the six winning possibilities of the event. So there 6/8 chance of wiining it. So there is 75% chance that they will not be sent to prison

Jack was brought into the rehabilitation unit last week. Three
weeks ago, he suffered a head injury in a car accident. He has been
referred to your office to determine the extent of his cognitive
damage. What tests and methods of assessment should you use in your
evaluation?

A statue on a pedestal is placed in a room with flat mirrors on
the parallel northern and southern walls, producing an infinite
number of images in each mirror. If the walls are 7.55 m apart and
the statue is 1.50 m from the northern wall, what are the distances
from the statue to the first four images formed in the northern
mirror?
first image =?m
second image= ?m
third image=?m
fourth image=?m

A 15 year old girl in a coma was brought to the emergency room
by her parents. She has been an insulin dependent diabetic for 7
years. Her parents stated that there have been several episodes of
hypoglycemia and ketoacidosis in the past, and that their daughter
has often been “too busy” to take her insulin injections. The
laboratory results obtained on admission are shown in Case study
Table 14-5.1
1. Calculate the osmolal gap.
2. What method was used...

On the midnight shift,
the number of patients with head trauma in an emergency room has
the probability distribution shown below.
x
0
1
2
3
4
5
Total
P(x)
.09
.32
.27
.17
.11
.04
1.00
(a) Calculate the mean and standard deviation.
(Round your mean value to 2 decimal places and standard
deviation to 3 decimal places.)

A plane mirror is placed 20° above the horizontal on
the corner of a room and another plane mirror is placed at the
vertical wall. Determine the angle of reflection made by the mirror
on the wall.

Michael, 23, is brought to the emergency room by ambulance. He
is alert, confused and uncooperative. He is also unable to follow
simple commands or answer simple questions. His girlfriend reports,
“We were at his house, studying. He just made this really strange
sound. Suddenly he is on the floor shaking and his eyes are rolled
back in his head. I turned him on his side. I don’t know what is
going on with him, but I did call his...

To practice Problem-Solving Strategy 21.1 Coulomb's Law. Three
charged particles are placed at each of three corners of an
equilateral triangle whose sides are of length 3.7cm . Two of the
particles have a negative charge: q1 = -7.7nC and q2 = -15.4nC .
The remaining particle has a positive charge, q3 = 8.0nC . What is
the net electric force acting on particle 3 due to particle 1 and
particle 2?
Part B
Find the net force ?F? 3...

To practice Problem-Solving Strategy 21.1 Coulomb's Law. Three
charged particles are placed at each of three corners of an
equilateral triangle whose sides are of length 3.7cm . Two of the
particles have a negative charge: q1 = -7.7nC and q2 = -15.4nC .
The remaining particle has a positive charge, q3 = 8.0nC . What is
the net electric force acting on particle 3 due to particle 1 and
particle 2?
Part B
Find the net force ?F? 3...

To practice Problem-Solving Strategy 21.1 Coulomb's Law.
Three charged particles are placed at each of three corners of
an equilateral triangle whose sides are of length 3.7 cmcm . Two of
the particles have a negative charge: q1q1 = -6.9 nCnC and q2q2 =
-13.8 nCnC . The remaining particle has a positive charge, q3q3 =
8.0 nCnC . What is the net electric force acting on particle 3 due
to particle 1 and particle 2?
Part C
Assume that...

To practice Problem-Solving Strategy 21.1 Coulomb's Law.
Three charged particles are placed at each of three corners of
an equilateral triangle whose sides are of length 3.7 cmcm . Two of
the particles have a negative charge: q1q1 = -6.9 nCnC and q2q2 =
-13.8 nCnC . The remaining particle has a positive charge, q3q3 =
8.0 nCnC . What is the net electric force acting on particle 3 due
to particle 1 and particle 2?
Part B
Find the...

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