Daniel plays two games in the casino. The first game he believes he has 60% chance to win. If he wins the first game, he will win the second game with 25% chance, if he loses the first game, he will win the second game with 75% chance. The winning prices for the first and second game are $1 and $2 respectively
A. What is the probability that he wins the second game?
B. If he wins the second game, what is the probability that he also won the first game?
C. What is the expected value for the price he wins from the two games? What is the variance of it?
Answers
Answer:
1) the probability that he wins the second game is 0.45
2) the probability he wins the first game given that he won the second game is 0.333
3) Expected Value is $ 1.5 and the variance is 0.75
Step-by-step explanation:
Given the data in the question;
Let Win1 represent first game victory
and Loss1 represent first game loss
Let Win2 denote second game victory
and Loss2 denote second game loss
now from the Tree diagram of Daniel;
P ( Win1 ) = 0.6
P ( Loss1 ) = 0.4
P ( Win2 | Win1 ) = 0.25
P ( Loss2 | Win1 ) = 0.75
P ( Win2 | Loss1 ) = 0.75
P ( Loss2 | Loss1 ) = 0.25
1) probability that he wins the second game will be;
P ( Win2 ) = [P ( Win1 ) × P ( Win2 | Win1 )] + [P ( Loss1 ) × P ( Win2 | Loss1 ) ]
we substitute
= [0.6 × 0.25] + [0.4 * 0.75] = 0.45
Therefore the probability that he wins the second game is 0.45
2)
If he wins the second game, what is the probability that he also won the first game will be;
{From Bayes' Theorem}
P ( Win1 | Win2 ) = P ( Win1 ) × P ( Win2 | Win1 ) / P ( Win2 )
= 0.6 × 0.25 / 0.45 = 0.333
Therefore the probability he wins the first game given that he won the second game is 0.333
c)
winnings probability
$0 0.4 × 0.25 = 0.1
$1 0.6 × 0.75 = 0.45
$2 0.4 × 0.75 = 0.3
$3 0.6 × 0.25 = 0.15
so Expected Value = ∑( winnings × individual win probability)
= (0 × 0.1) + (1 × 0.45) + (2 × 0.3) + (3 × 0.15)
= 0 + 0.45 + 0.6 + 0.45
= $ 1.5
Variance = ∑( X² ) - (∑(X))²
∑( X² ) = Summation of ( Winnings² × Probability of Each Win )
so
Variance = 0 × 0 × 0.1 + 1 × 1 × 0.45 + 2 × 2 × 0.3 + 3 × 3 × 0.15 - ( 1.5 )²
Variance = 0 + 0.45 + 1.2 + 1.35 - 2.25
Variance = 3 - 2.25
Variance = 0.75
Therefore Expected Value is $ 1.5 and the variance is 0.75
Related Questions
Is this a function???
Answers
Answer:
pfft no lol
Step-by-step explanation:
yeah no
have a good day! :)
plz give me brainliest
Answer:
yes
Step-by-step explanation:
i think,because it goes past the center it all
Help anyone
8th grade math need it asap
Answers
Answer:
[tex] \frac{7}{10} [/tex]
Answer:
7/10
Step-by-step explanation:
If you move the decimal point to over to the right, also known as multiplying by a hundred, then you get 70. Right now we have 70/100
Simplify even further you would get 7 / 10
if 7/12 is multiplied by a fraction less than 1 what would be the product
Answers
Answer:
Examples below
Step-by-step explanation:
We have the fraction
[tex]\frac{7}{12}[/tex]
It's required to multiply it by any fraction less than 1. Let's select the following fractions. All of them are less than 1 because the numerator is less than the denominator:
[tex]\frac{1}{7}[/tex]
[tex]\frac{4}{5}[/tex]
[tex]\frac{6}{35}[/tex]
The required products are:
[tex]\frac{7}{12}\cdot \frac{1}{7}=\frac{7}{7*12}=\frac{1}{12}[/tex]
[tex]\frac{7}{12}\cdot \frac{4}{5}=\frac{4*7}{12*5}=\frac{7}{15}[/tex]
[tex]\frac{7}{12}\cdot \frac{6}{35}=\frac{6*7}{12*35}=\frac{1}{10}[/tex]
-2.5(4w-4)= -6 and check
Answers
Answer:
y=60
Step-by-step explanation:
sophia used 1/10 of a liter of water to fill 1/4 of a fish aquarium. How much water, in liter is required to fill the aquarium?
Answers
Answer:
4/10 of a liter
Step-by-step explanation:
if 1/10 of a liter fills 1/4 of the aqauium then your ratio is .1:.25 out of 100 so
100/25=4
What basic fact can you use to divide 2,800 by 7
Answers
Step-by-step explanation:
2800/7 = 400, ,
please you can see the upper paper which
can to solve this division math
What is 3×7×7×7×7 using index notation
Answers
Answer: 3 x 7^4
Because there's one 3 & four 7's .
Step-by-step explanation:
Evaluate -5-15+4+15−5−15+4+15minus, 5, minus, 15, plus, 4, plus, 15.
Answers
Answer:
-2
Step-by-step explanation:
ur welcome
-1
Step-By step Explanation:
what is the relationship of the angles
Answers
Answer:
Alternate Interior Angles
Answer:
a
Step-by-step explanation:
which of the following is a characteristic of the circumcenter of a triangle? multi-choice. A. it is the center of the only circle that can be inscribed in the triangle. , B. it is the center of the circle that can be inscribed in given a given triangle. C. it is the center of the only circle that can be circumscribed about the triangle. D. it is equidistant from all three sides of the triangle.
Answers
Answer:
C
Step-by-step explanation:
The circumcenter is called ”the circumcenter” because it is the center of the circle that ”circumscribes” the triangle.
I hope this helps!
Further explanation:
For a circle to circumscribe something, it circles it so that each of the vertices are on the circle, so each of the vertices are equidistant from the circumcenter. The circumcenter of a triangle is formed by the perpendicular bisectors of its sides.
Side note:
The rest of the choices describe an incenter.
HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.
Stats question, I'm really stck please help me!
Answers
Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
What is the quotient of 4/5 divided by 17/9
Answers
Answer:
0.42352941176
Step-by-step explanation:
hope this helps
The value of quotient will be 0.42.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
''4/5 divided by 17/9''
Now,
Since, The expression is,
''4/5 divided by 17/9''
Hence, After solving we get;
⇒ 4/5 ÷ 17/9
⇒ 4/5 × 9/17
⇒ 36/85
⇒ 0.42
Thus, The value of quotient = 0.42
Learn more about the divide visit:
brainly.com/question/844312
#SPJ2
Hewo plz help can u answer
PUT A REAL ANSWER!!!!!!!!!!
5 pts.
175+8w≥425
Answers
Answer:
w≥31.25
Step-by-step explanation:
175+8w≥425
-175 -175
8w≥250
/8 /8
w≥31.25
Answer:
X is greater than or equal to 125/4
Step-by-step explanation:
Subtract 175 from both sides which will turn 425 into 250
Divide 8 from 8x to the other side to turn 250 into 125/4
In the end, you get X is greater or equal to 125/4
Which of the three ordered pairs represent the
unit rate?
(1,4)
(3, 12)
(2,8)
Answers
Answer:
(1,4)
Step-by-step explanation:
That's the rate that each coordinate point goes up by as well as it's the first point in the table
Which line is parallel to y = -5/2x - 7?*
O 2x + 5 y = -5
O 2x - 5 y = 30
O 5x + 2y = 4
O 5x-2y = 8
Answers
Answer:
the answer is
5x + 2y = 4
Hello there ^^ I'd love it if you would help me :D
Answers
Answer:
Great question
Step-by-step explanation:
Where is it :p
Least to greatest 0.4, 5/8, 74%, 3/5
Answers
Answer:
0.4,3/5,5/8,74%
Step-by-step explanation:
Change them all into decimals.
Get 0.4,0.625,0.74,0.6
Then reorder and see what their original values were
Which expression is equivalent to one over three p + 15?
one over three(p + 45)
one over three(p + 5)
3(p + 45)
3(p + 5)
Answers
Answer:
1/3p + 5
Step-by-step explanation:
1/3 of 15 is 5
If you think in terms of multiplication: 3 groups of 5 is 15 so 1 group of 15 would be 5
Answer:
a) 1/3 (p+45)
Step-by-step explanation:
that's the answer
Colin invests £14100 into his bank account. He receives 9.0% per year simple interest. How much will Colin have after 5 years? Give your answer to the nearest penny where appropriate.
Answers
Answer:
6350
Step-by-step explanation:
What is 2-1x(57\7) ?
Answers
Answer:
2 - [tex]\frac{57}{7}[/tex]x
Step-by-step explanation:
2-1x(57/7)
2 - [tex]\frac{57}{7}[/tex]x
Help me out please don’t pass this question help me !
Answers
Answer:
20L + 45 = 225
Step-by-step explanation:
20 is the slope making it constant
45 is a one time fee making it a y intercept
equaling 225
Answer:
20L+45=225
Step-by-step explanation:
20 represents how much she paid for each lesson, we don't know how many lessons she paid for so we use the variable L and multiply it by 20. She only had to pay the registration fee once so 45. Unknown lessons taken by 20 + the one-time fee of 45 equals 225
Hope this helps!
Identify proportional relationships
Does the following table show a proportional relationship between the variables g and h?
g
3
6
9
9
36
81
Answers
Answer:
sure easy man the carrot is blue and green and orange there naswer soled
HELP!!!! 2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
The dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching television each week. What are the mean and median?
The 5th-grade mean is
.
The 7th-grade mean is
.
The 5th-grade median is
.
The 7th-grade median is
.
Answers
Answer:
5th grade mean - 4.67
7th grade mean - 3.46
5th-grade median - 5
7th-grade median - 3.5
makayla is painting her house.each room needs 1/2 gallon of paint if she has three gallons of paint,how many rooms can she paint?
Answers
Answer:
6 rooms.
Step-by-step explanation:
3 x 2 = 6
it takes 2 halves to make a whole so 3 x 2 = 6
Suppose that an individual has a body fat percentage of 12.7% and weighs 132 pounds. How many pounds of his weight is made up of fat? Round your answer to the nearest tenth.
Answers
Answer:
just go with your heart
Kellen got an e-mail from his bank on June 7th, June 21st, July 5th, and July 19th. Use inductive reasoning to predict the next time Kellen will receive an e-mail from his bank. A. July 21st B. July 26th C. August 2nd D. August 3rd
Answers
Answer:
August 2nd
Step-by-step explanation:
31 days in july, last email on the 19th
19-5=14
31-19=12
12+2=14
August 2nd, please mark brainliest
Explanation:
From:
07/06 to 21/06 is a total of 14 days
21/06 to 05/07 is also a total of 14days
05/07 to 19/07 also took 14 days
Therefore, the next email will be sent in another 14 days which is August 2nd (02/08)
Brooke measures the height of her bean plant for a science project. The bean plant is 12.5 inches tall.
How many centimeters tall is Brooke’s bean plant?
Answers
Answer:31.75 centimeters
Step-by-step explanation:
Which function is represented by this graph
Answers
y=-1/2x +3 it's last one
What is MR? Explain.
Answers
Answer:
MR is 20 because if the side lengths that are shown are congruent, then the bottoms are too. so each part of the bottom that has a number, that number repeats on the part that's part of that triangle. so the bottom lengths go " 4 6 6 4" and you add those together and get 20
god please help me i’ve been stuck on this problem for hours and i’m so hungry:(
Answers
Answer:
B
Step-by-step explanation:
u should go eat
Answer:
A)
because it passes the line twice instead of once
(fuctions only cross once)
hope that helped you:)
please make my answer brainiest as im trying get 3 brainiest answers