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
Helppp pleaseee, abc= dce. If ac=5 and bc=7 cd=?
Answers
Answer:
CD = 5
Step-by-step explanation:
Given that ∆ACB is congruent to ∆DCE, it follows that their corresponding angles and corresponding side lengths are congruent to each other. Thus:
AC is congruent to CD,
BC is congruent to EC, and
AB is congruent to DE.
Since AC = 5, therefore CD = 5.
PICTURE BELOW....................
Answers
Answer: C
Step-by-step explanation: 45 divided by 18 is 2.5
57.351 rounded to the ones place
Answers
How do you round to the ones place?
Look to the next smallest place value, the digit to the right of the place value you're rounding to. For example, if you want to round to the nearest ten you'd look at the ones place. If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round to as-is.
Answer:
Step-by-step explanation:
do u mean round to the nearest 10th as in one decimal place or to the nearest one not decimal place?
What is the equation of the line that has a slope of -3 and passes through the point (-2, 4)?
O y = -3x - 2
y=-3x
ООО
y=-3x - 4
y = -3x + 4
O y=-3x + 2
Answers
Plug in points
4 = -3(-2) + b
4 = 6 + b, b = -2
Solution: y = -3x - 2
Find the slope of the line represented by the table
Answers
Answer:
slope = 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 8) and (x₂, y₂ ) = (1, 2) ← 2 ordered pairs from the table
m = [tex]\frac{2-8}{1-3}[/tex] = [tex]\frac{-6}{-2}[/tex] = 3
Which diagram demonstrates the problem 3x 1/4
Answers
Answer:
A.
Step-by-step explanation:
3 * 1/4 = 3/4
Which answer shades 3 out of 4 blocks? A.
Answer:
the answer is A
Step-by-step explanation:
3 * (1/4) = .75.... Think about how many quarters make a dollar .75 cents is 3/4 of a dollar
In which situation would it be appropriate to use square feet as a measurement?
Answers
Answer:
The correct answer is B ; Karla must determine the area of a floor in her house.
plz help !!!!! complete the function tables then graph
Answers
Answer:
Step-by-step explanation:
Which of the following represents a reflection of (-3, 4) across the y-axis?
(-4, 3)
O (-3,-4)
O (3, 4)
O (4, -3)
Answers
Please help me 20 points!!!!!
Answers
Answer:
A. 0.4 km
B. 48 fruits to 12 vegetables
C. 72 hours
60%
Step-by-step explanation:
1 km = 1000 m
You have 400 m
1000m/1km = 400m/1000m
400/1000
0.4km
4:1
Ok so an easy way to do this one is multiplication.
you need the number of fruits to be 4 times more than the number of vegetables.
A would be 2:1 because 16 is 2 times more than 8
B would be 4:1 because 48 is 4 times more than 12
C would be 8:1 because 24 is 8 times more than 3
D would be 3:1 because 60 is 3 times more than 20
B would be the correct answer
If they traveled 216 miles in 3 hours, to find average you have to divide miles by hours.
216/3
72 hours
The tigers won 12 of their last 20 games.
12/20
0.6
Percent is 100 times the decimal.
0.6*100
60%
Don't be afraid to reach out with any more questions! I hope this helps!
Question 3
And question 4 pleaseeee help!!
Answers
Answer:
see pdf
Step-by-step explanation:
Which symbol will make the number sentence true?
Answers
Answer:
<
Step-by-step explanation:
8/11=0.72727272727272727272727272 just repeated over and over again so its less
Answer:
b
Step-by-step explanation:
Find the original price of a pair of shoes if the sale price is $63 after a 30% discount.
Answers
Answer:
$90
Step-by-step explanation:
To find the original price, divide 63 by 0.7:
63/0.7
= 90
So, the original price is $90
Answer:
$90.00
Step-by-step explanation:
First of all let x be the price of the pair of shoes that you are trying to find.
next since we have 30percent off that price we have
x - 0.30x = 0.70x
which in turn is equal to 63 dollars
so our expression is
0.70x = $63
x = 63 / 0.70
= $ 90.00
10. DESIGN Mr. Hagarty is choosing tiles to design a kitche backsplash for a rectangular area 65 inches wide and 9 in tall . Design a backsplash using each type of rhombi-shape tile that minimizes cost. a. diagonals of 1 inch and 1.5 inches, $0.05 each b. diagonals of 1.5 inches and 2 inches, $0.07 each Areas of Trapezoids, Rhombi, and Kites 2 © B O DO
Answers
Answer:
I honeslty dont know I just need points to answer a question
Step-by-step explanation:
hope you find the answer youre looking for!
how do i right the half of x pls help will give brainliesst answer
Answers
Answer:[tex]\frac{1}{2}[/tex]x or x/2
Step-by-step explanation:
write an equation of a line that is perpendicular to given line that passes through the given point 5y+2x=-15 T(5,-5)
Answers
Step-by-step explanation:
The answer is on the bottom if you just wanna scroll down.
The first thing that you would want to do is turn the equation of the given line into slope-intercept form (it's just easier). To do that, you would want to isolate y on either side. So subtract 2x and divide both sides by 5 and you get: y=-2/5x-3. After you do this, remember that perpendicular lines have the negative reciprical slope of the original line. So since the slope is -2/5, the slope of a perpendicular line would be 5/2. Now you have m=5/2 which is your slope! Now you can use slope point form which is y-y_1=m(x-x_1). You know your m which is 5/2. y-y_1=5/2(x-x_1). Since we know that the line passes through the point (5,-5) we can just plug the numbers in. y-(-5)=5/2(x-5). simplify everything: y+5=5/2(x-5). Remember, math is all about making things simple and easy. since the problem didn't say a specific type of equation, you can just put that as your answer!
Answer:
y+5=5/2(x-5)
Hope this helps! (If it's wrong, plz leave sum comments. thx lol)
which statement is true regarding the functions on the graph?
Answers
Answer:
f(3)=g(3)
Step-by-step explanation:
the only one i see is that
f(3)=g(3)
because the two functions intersect there
that means the two values are the same
WHATS THE ANSWER HELP
Answers
can someone help me with this
Answers
Answer:
30
Step-by-step explanation:
3 + (6 * 4) + 3 = 30
hope this helps
2 mi = ____ ft Please help! :((
Answers
Answer:
2 mi = 10560 ft
Step-by-step explanation:
you coulve searched it up
Answer:
you multiply it by 2 so its 10560
F(x)=x/2 +8, what is f(x) when x = 10?
4
ОООО
13
36
Answers
Answer:
13
Step-by-step explanation:
Just replace x with 10, so F(10) = 10/2 + 8. Which is 5 + 8.
can u pls help me with this question
Answers
Answer: a or d
Step-by-step explanation:
How many 2-inch cubes are needed to completely fill a cubic box that measure 8 inches.
Answers
Answer:
It will be 64 cubes.
Step-by-step explanation:
if one side is 8 inches then 8/2 is 4
to fill one face, 4 × 4 = 16
to fill a cube 16 × 4 = 64
Answer: 64 cubes will fit
Mary is 3 years older than twice her brother's age, a. Which expression
represents Mary's age?
A. 2a + 3
B. 2a - 3
C. 3a + 2
D. 3a - 2
Answers
Answer:
C. 3a + 2
Step-by-step explanation:
brainiest plz
explanation: if she’s 3 years older you will have to add that on to the brothers age (a) and a needs to be multipled by 2 cuz it says twice than
A snail can crawl 2/5 of a meter in a minute.
How many minutes will it take the snail to crawl 6 meters?
Please give me an answer A S A P.
Answers
6/0.4= 15
The snail crawls .4 meters per minute and .4*15=6
Is each graph a function or not?
Answers
Answer:
IN THIS ORDER
NO
NO
YES
YES
NO
YES
Step-by-step explanation:
Hope this helped if I got it wrong, sorry ill edit it if I did :)
Last year, Jeffrey grew 5/8 of an inch and his brother grew 1/2 of an inch. How much more
did Jeffrey grow than his brother?
Simplify your answer and write it as a fraction or as a whole or mixed number.
Answers
Answer:
Jeffrey grew 1/8 inch more than his brother
Step-by-step explanation:
5/8 - 1/2 = 5/8 - 4/8 = 1/8
Answer:
[tex]\frac{5}{4}[/tex] [tex]or[/tex] [tex]1.25[/tex]
Step-by-step explanation:
[tex]\frac{5}{8}[/tex] ÷ [tex]\frac{1}{2}[/tex] = [tex]?[/tex]
[tex]\frac{5}{8}[/tex] = [tex]0.625[/tex]
[tex]\frac{1}{2}[/tex] = [tex]0.5[/tex]
[tex]\frac{0.625}{0.5}[/tex] = [tex]\frac{5}{4}[/tex]
[tex]Therefore,[/tex] [tex]\frac{5}{4}[/tex] [tex]is[/tex] [tex]the[/tex] [tex]answer.[/tex]
Hope this helps! <3
Which equation should you solve to find x?
Answers
Answer:
B
Step-by-step explanation:
[tex]sin ~26^\circ=\frac{x}{10}[/tex]
Answer:
sin 26 = x/10
Step-by-step explanation:
A cookie factory uses 1/10 of a barrel of oatmeal in each batch of cookies. The factory used
2/5 of a barrel of oatmeal yesterday. How many batches of cookies did the factory make?
Answers
Answer:
4
Step-by-step explanation:
2/5 is the same as 4/10
the answer below thanks
Answers
Answer:
The equation of the circle having centre (-5,-9) and radius r=3 is
x² + 10 x +y² + 14 y + 65 = 0
Step-by-step explanation:
Explanation:-
From graph The centre of the circle C( -5 , -7)
The radius of the circle r = 3cm from the centre of the given circle
The equation of the circle
From graph the centre ( h, k) = ( -5,-7) and r = 3cm
[tex](x-(-5))^2+(y-(-7))^2 = 3^2[/tex]
x² + 10 x +25 +y² + 14 y + 49 =9
x² + 10 x +25 +y² + 14 y + 49 -9=0
The equation of the circle
x² + 10 x +y² + 14 y + 65 = 0