Suppose that Haley encounter two traffic lights on her commute to GGC campus. Based on
her past experience, she judge that the probability is 0.35 that the first light will be red when she gets to it,
0.45 that the second light will be red, and 0.20 that both lights will be red. Let R1 denote the event that the
first light is red, and let R2 denote the event that the second light is red.
a) Determine the probability that at least one light will be red. (Show how you calculate this.)
b) Determine the conditional probability that the second light will be red given that the first light is
red. (Show how you calculate this.)
c) Are the events R1 and R2 independent? Justify your answer numerically.
d) Are the events R1 and R2 disjoint (mutually exclusive)? Justify your answer numerically.
Answer:
Explained below.
Step-by-step explanation:
The information provided is,
P (R₁) = 0.35
P (R₂) = 0.45
P (R₁ ∩ R₂) = 0.20
(a)
Compute the probability that at least one light will be red as follows:
P (at least one light will be red) = P (R₁ ∪ R₂)
= P (R₁) + P (R₂) - P (R₁ ∩ R₂)
= 0.35 + 0.45 - 0.20
= 0.60
Thus, the probability that at least one light will be red is 0.60.
(b)
Compute the conditional probability that the second light will be red given that the first light is red as follows:
[tex]P(R_{2}|R_{1})=\frac{P(R_{1}\cap R_{2})}{P(R_{1})}[/tex]
[tex]=\frac{0.20}{0.35}\\\\=0.571428\\\\\approx 0.57[/tex]
Thus, the conditional probability that the second light will be red given that the first light is red is 0.57.
(c)
If two events, say A and B are independent then:
P (A|B) = P (A).
The value of P (R₂ | R₁) = 0.57.
And the value of P (R₂) = 0.45
P (R₂ | R₁) ≠ P (R₂)
Thus, the events R₁ and R₂ are not independent.
(d)
If two events, say A and B are mutually exclusive then:
P (A ∩ B) = 0
The value of P (R₁ ∩ R₂) = 0.20.
Thus, the events R₁ and R₂ are not mutually exclusive.
solve the following equation 5+7=11+7
Answer:
The equation, 5+7=11+7 solved step by step is:
5 plus 7, which equals 12.
And then, 11 plus 7, which equals 18.
You put it all together, it turns into 12=18 which isn't true.
So, your problem is not real.
Step-by-step explanation:
Your question has no answer because the two sides aren't equal.
Hope this helped! :)
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A falcon flew 70 miles in 3 hours. What was the speed of the falcon?
speed = distance over time ; 1 mile = 1609 meters.
Answer:
10.4 meters per second i think?
Step-by-step explanation:
The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
Answer:
I think it might be zero
Step-by-step explanation:
you might want to look into this all the way beforyou trust put it into*
A company has developed a new type of light bulb and wants to estimate its mean lifetime. A simple random sample of 100 bulbs had a sample mean lifetime of 750.2 hours with a sample standard deviation of 30 hours. Construct a 98% confidence interval for the population mean lifetime of all bulbs manufactured by this process.
Answer:
hh
Step-by-step explanation:
JHWKHvksdhvdsjKdsk
helpppppppppppppppppp
how much was the second one?
What is the total number of digits required in numbering the pages of a book, which has 1,150 pages?
Caroline wants to buy a pair of shoes that has an original price of $50.00. She has a coupon for a 40% discount off of the original price. What is the final
cost for Caroline's shoes?
А
$10
B
$20
С
$30
ОО
D
$48
Answer:
your new should be c $20
The final cost is $30.
Option C is the correct answer.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The original price of the coat = $50
Discount = 40%
Now,
The final cost.
= (100 - 40)% of 50
= 60% x 50
= 60/100 x 50
= $30
Thus,
The final cost is $30.
Learn more about percentages here:
https://brainly.com/question/11403063
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Select the
Suppose Phil reads a book that contains 16 conspiracy theories. When he researches the
theories, he finds that 75% of them are false. How many of the theories are true?
Answer:
4 of the conspiracy theories were true
Step-by-step explanation:
Percentages
Phil read a book with 16 conspiracy theories, 75% of which were false. It means that 25% of them were true.
25% of 16 is 25 * 16 / 100 =400 / 100 = 4
Thus, 4 of the conspiracy theories were true
Name all rays with endpoint E
Answer: Is there an image??
AE, BE, CE, and DE is the rays with endpoint E.
What is a vector?An item with both magnitude and direction is referred to be a vector.
A vector can be visualized geometrically as a straight spline, with a pointing in the orientation and a length equal to the value of the vector.
Geometrical objects with magnitude and direction are called vectors.
A line with an arrow in its direction can also be used to represent a vector, and the length of the line relates to the vector's amplitude.
Given the figure,
The endpoint of all rays is E.
The rays associated with point E are;
AE, BE, CE, and DE
Hence "AE, BE, CE, and DE is the rays with endpoint E".
For more information about vector,
brainly.com/question/13322477
#SPJ2
It took Jesse 195 minutes to write an essay for school.
How many hours did it take Jesse to write the essay for
school?
Answer: 3 hours and 15 minutes
Step-by-step explanation:
Answer:
Time taken by Rahm to write the essay and finish the science project = 12.5 hours
Step-by-step explanation:
Now, we need to find the total time spent by Rahm to finish the both writing the essay and the science project.
Hence, Time taken by Rahm to write the essay and finish the science project = 12.5 hours
How many proportional relationships are shown in the coordinate plane below? Please answer quick
Answer:
The answer is 1
Step-by-step explanation:
There is 1 proportional relationship in the graph
Hello, I wanted to leave you this photograph of mathematics that I think will be very useful to some of you, observe it
Answer:
yes
Step-by-step explanation:
Answer:
thank you
Step-by-step explanation:
:)
Ivan has 32 baseballs and 48 basketballs. If he wants to divide them into identical groups without any balls left over, what is the greatest number of groups Ivan can make
Here we will show you step-by-step with detailed explanation how to calculate 48 divided by 32 using long division.
Before you continue, note that in the problem 48 divided by 32, the numbers are defined as follows:
48 = dividend
32 = divisor
Step 1:
Start by setting it up with the divisor 32 on the left side and the dividend 48 on the right side like this:
3 2 ⟌ 4 8
Step 2:
The divisor (32) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:
0
3 2 ⟌ 4 8
Step 3:
Multiply the divisor by the result in the previous step (32 x 0 = 0) and write that answer below the dividend.
0
3 2 ⟌ 4 8
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.
0
3 2 ⟌ 4 8
- 0
4
Step 5:
Move down the 2nd digit of the dividend (8) like this:
0
3 2 ⟌ 4 8
- 0
4 8
Step 6:
The divisor (32) goes into the bottom number (48), 1 time(s). Therefore, put 1 on top:
0 1
3 2 ⟌ 4 8
- 0
4 8
Step 7:
Multiply the divisor by the result in the previous step (32 x 1 = 32) and write that answer at the bottom:
0 1
3 2 ⟌ 4 8
- 0
4 8
3 2
Step 8:
Subtract the result in the previous step from the number written above it. (48 - 32 = 16) and write the answer at the bottom.
0 1
3 2 ⟌ 4 8
- 0
4 8
- 3 2
1 6
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 48 divided by 32 calculated using Long Division is:
1
16 Remainder
a child walks 3/10 of a mile in 1\5 hour. At this rate, how far will the child walk in 1 hour
Answer:
1½ mile
Step-by-step explanation:
Given
3/10 mile = ⅕ hour
Required
Determine the distance in 1 hour
Since rate is constant, we have:
3/10 mile = ⅕ hour
Multiply both sides by 5
5 * 3/10 mile = ⅕ hour * 5
15/10 mile = 5/5 hour
3/2 mile = 1 hour
1½ mile = 1 hour
Hence,the child will walk 1½ mile in 1 hour
The set {1,2,3,4,...} is called the set of
This is an example of a finite set
I hope this is the answer you're looking for :)
A day care center has 52 children. Each teacher has the same number of children. How many children could each teacher at the center have.
Answer:
The answer to this question would depend on how many teachers are available in the day care center.
If every teacher is to have the same number of children then the number of teachers will be factors of 52 which are more than 1;
2, 4, 13, 26, 52
If there are 2 teachers, each teacher will have 26 children
If there are 4 teachers, each teacher will have 13 children
If there are 13 teachers, each teacher will have 4 children
If there are 26 teachers, each teacher will have 2 children
If there are 56 teachers, each teacher will have 1 child
What is 6√2⋅√11−2√22 expressed in simplified form?
Hope this help you!!! :))
Period of y=2tan (2x+90) -1
I need help !!!!!!!
Given , KM = 22
Then JL =
This trapezoid is an isosceles trapezoid which means its diagonals will be equal . So ,
KM = JL ( the diagonals in an isosceles trapezoid are congruent )
22 = JL
JL = 22
Therefore , JL = 22 .
Solution (6) :Given , DF = 8.7
Then , EG =
Since this trapezoid is an isosceles trapezoid , its diagonals will be equal . So ,
DF = EG ( the diagonals in an isosceles trapezoid are congruent )
8.7 = EG
EG = 8.7
Therefore , EG = 8.7 .
Identify the coefficients: -3h - 2h + 6h +9
Answer:
its -3h,-2h,6h
Step-by-step explanation:
hope i helped
7 + (−3) simplify
please
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
When you add a negative number, you're basically subtracting it.
7 - 3 = 4
Hope this helps! Good luck :)
Louis deposited $300 into his bank account. She now has $4501. Enter and solve an equation to find how much was in his account before the deposit. Let it represent the variable.
Answer: $4,201
Step-by-step explanation: 4,501 - 300 = 4,201
Answer:
d+300=4501
Step-by-step explanation:
Take the total: 4501 and subtract it by the amount of money he deposited the second time: 300 and that will show you the missing amount he had in his account before the deposit.
4501-300=4201
Find each value for the geometry triangles below
Answer:
14. x=18
Step-by-step explanation:
For 14 you can see that all the angles must add up to 180.
Setup the equation 5x+2x+x=180 and solve for x
For 15 do the same thing, add up all of the lengths and substitute the missing one as W. Set them equal to 360 and you should get your answer.
Find the integers that are closest to 65 (the number in the middle)
Step-by-step explanation:
Divisors of the Positive Integer 65:
1,5,13,65
Sum of all the Divisors of 65, including itself:
84
Sum of the Proper Divisors of 65:
19
Properties of the number 65:
The integer 65 is an odd number.
The integer 65 is a Composite number.
19 is less than 65, so 65 is a deficient number.
If A= (-1,-3) and B= (11,-8) what is the length of AB?
Answer:
AB is 13
Step-by-step explanation
Charlie has 468 onions to sell. He puts 12 onions in each bag, and he sells the bags for $8 each. What is the answer?
Answer:
312 $
Step-by-step explanation:
468 / 12 = 39 bags
8 x 39 = 312 $
so the answer is 312$
Tim used the expression n3 to determine the volume of a cube where n represents a side length of the cube. Using this expression, what is the volume, in cubic inches, of a cube with a side length of 3.5 inches?
Answer:
4
Step-by-step explanation:
Answer:
Step-by-step explanation:
What’s 1 times 5 times 2?
Answer:
10
Step-by-step explanation:
Answer:10
Step-by-step explanation:1×5=5×2=10