An experiment consists of ranomly drawing three cards in succession without replacement from a standard deck of 52 cards. Let A be the event of a king on the first draw, B the event of a king on the second draw, and C the even of a king on the third draw. Describe each of the events listed below and calculate its probability.
a. A ∩ B
b. A U B
c. A ∩ B ∩ C
d. A U B U C
Answer:
0.0045248 ;
0.1312218 ;
0.0001809 ;
0.1659729
Step-by-step explanation:
Number of Kings in deck = 4
Total number of cards in deck = 52
Picking without replacement :
A = King on first draw :
P(A) = 4 / 52
A = King on 2nd draw :
P(B) = 3 / 51
A = King on 3rd draw :
P(C) = 2 / 50
1.) P(A n B) = P(A) * P(B)
P(A n B) = 4/52 * 3/51 = 12 / 2652 = 0.0045248
2.) P(A u B) = P(A) + P(B) - P(AnB)
P(AuB) = 4/52 + 3/51 - 0.0045248 = 0.1312218
3.) P(A ∩ B ∩ C) = P(A) * P(B) * P(C)
P(A ∩ B ∩ C) = 4/52 * 3/51 * 2/50 = 0.0001809
4.) P(A U B U C) =
P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) - P(AnBnC)
P(AnC) = P(A) * P(C) = 4/52 * 2/50 = 0.0030769
P(BnC) = P(B) * P(C) = 3/51 * 2/50 = 0.0023529
4/52 + 3/51 + 2/50 - 0.0045248 - 0.0030769 - 0.0023529 + 0.0001809 = 0.1659729
what does math means
Answer:
It means mathematics.
Lamoo thats wht it said in go-ogle
Step-by-step explanation:
Crystal receives a monthly salary of $3,980. Find her earnings per year and earnings per week.
Answer:
per year: $47,760 per year
per week: $918.46 per week
Step-by-step explanation:
$3980 per month x 12 months = $47,760 per year
$47,760 per year divided by 52 weeks = $918.4615384615
Since we're talking money, let's round off our answer to the hundredths place ($918.46 per week)
Double check our answer (918.46 x 52 = 47,760) great!
Answer:
47760 per year
918.46154 per week
Step-by-step explanation:
$3,980 x 12= $47760
$47760/52= $918.46154
One circle has a diameter of 6 inches. A second, larger circle has a diameter that is four times the diameter of the first circle. What is the ratio of the area of the smaller circle to the larger circle?
A 2:3
B 1:6.4
C 1:16
D 1:64
Answer:
Step-by-step explanation:
d₁ = 6 inches
r₁ = 3 inches
area = πr₁² = 9π in²
d₂ = 24 inches
r₂ = 12 inches
area = πr₂² = 144π in²
ratio of areas = (9π)/(144π) = 9/144 = 1/16
100 POINTS!!!
Reggie went out to eat with his family.
The cost of their food was $48.50, plus Reggie gave the waiter an 18% tip.
What was the total price of their meal, including the food and the tip!
A. $57.23
B. $48.68
C. $87.30
D. $50.30
Answer:
A) $57.23
Step-by-step explanation:
0.18 x 48.5= $57.23. Hope this helped!
Which is greater 1/4 or .25
Answer:
they are both the same equal
Step-by-step explanation:
can i get brainliest
I need help pleaseeeee
Answer:
The value will be positive because there are five minus signs which means negative but the there are two minus before the biggest number which means positive.
Which system has no solution? A b c d
-X – 3, solve for a when g(x) = 6.
PLSSS
The length of a rectangular rug is 4 less than twice its width. The perimeter of the rug is 40 feet. What is the area of the rug?
1) 96 sq ft
2) 56 sq ft
3) 104 sq ft
4) 86 sq ft
Enter range of values for x
Answer:
42=3x+15
42-15+3x
27/3 = 9
Step-by-step explanation:
There are 31 students in a class.
The only languages available for the class to study are French and Spanish.
17 students study French.
15 students study Spanish.
6 students study neither French nor Spanish,
Using a Venn diagram, or otherwise, work out how many students study only one
language.
Answer:
24 students where studying one language
Step-by-step explanation:
which is more, 6 miles or 31,678 feet ?
Answer: 6miles
Step-by-step explanation: 6miles = 31680ft so 31680>31678
Suppose that 3\%3%3, percent of over 200{,}000200,000200, comma, 000 books borrowed from a library in a year are downloaded. The librarians plan to take an SRS of 757575 books from the population of borrowed books to see what proportion of books sampled are downloaded. What are the mean and standard deviation of the sampling distribution of the proportion of downloaded books
Answer:
The mean of the sampling distribution of the proportion of downloaded books is 0.03 and the standard deviation is 0.0197.
Step-by-step explanation:
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
3% of books borrowed from a library in a year are downloaded.
This means that [tex]p = 0.03[/tex]
SRS of 75 books.
This means that [tex]n = 75[/tex]
What are the mean and standard deviation of the sampling distribution of the proportion of downloaded books
By the Central Limit Theorem
Mean: [tex]\mu = p = 0.03[/tex]
Standard deviation: [tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.03*0.97}{75}} = 0.0197[/tex]
The mean of the sampling distribution of the proportion of downloaded books is 0.03 and the standard deviation is 0.0197.
Select the correct equation and correct answer to
solve for x using the triangle below.
Q
L
K
2x - 15
R
Р P.
2x - 8
Answer:
11
Step-by-step explanation:
LK = 1/2RP
theorem: straight line joining the midpoints of two sides of a triangle is parallel to the third side and equal to half the length of the third side.
LK = 2x - 15 ; RP = 2x - 8
2x - 15 = 1/2(2x - 8)
2x - 15 = 2x - 8/2
2x - 15 = x - 4
Collect like terms and simplify
x = 11
Evaluate 7y - 2
when y = 9
Answer:
The answer is 61.
Step-by-step explanation:
7(9)-2
63-2
61
Answer:61
7*(9)-2
63-2
61
Hope it's useful
In which areas did Franklin Roosevelt’s programs increase the power and role of the federal government?
the economy of the U.S. and of other countries
government ownership of business and industry
the lives of citizens and religious organizations
the economy and the lives of citizens
Answer:(1) reduce border conflicts with Canada
(2) increase acceptance of minorities within the
United States
(3) encourage Germany and the Soviet Union to
resolve their differences
(4) improve relations with Latin America
Step-by-step explanation:
think its B good luck
Need help finding angle A,B,C,D!!
What dose that sing mean before the square root mean and also what is the answer
The thing before the square root means that the answer can be positive and negative.
The manager of a music store has kept records of
The manager of a music store has kept records of the number of CDs bought in a single transaction by customers who make a purchase at the store. The accompanying table gives six possible outcomes and the estimated probability associated with each of these outcomes for the chance experiment that consists of observing the number of CDs purchased by a randomly selected customer at the store.
Number of CDs purchased 1 2 3 4 5 6 or more
Estimated probability 0.30 0.25 0.20 0.15 0.05 0.05
(a) What is the estimated probability that the next customer purchases three or fewer CDs?
(b) What is the estimated probability that the next customer purchases at most three CDs?
How does this compare to the probability computed in part (a)?
greater than part (a)less than part (a) the same as part (a)
(c) What is the estimated probability that the next customer purchases five or more CDs?
(d) What is the estimated probability that the next customer purchases one or two CDs?
(e) What is the estimated probability that the next customer purchases more than two CDs?
Answer:
(a) [tex]P(x\le 3) = 0.75[/tex]
(b) [tex]P(x\le 3) = 0.75[/tex]
(b) is the same as (a)
(c) [tex]P(x \ge 5) = 0.10[/tex]
(d) [tex]P(x = 1\ or\ 2) = 0.55[/tex]
(e) [tex]P(x > 2) = 0.45[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{CDs} & {1} & {2} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.30} & {0.25} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}[/tex]
Solving (a): Probability of 3 or fewer CDs
Here, we consider:
[tex]\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x\le 3) = P(1) + P(2) + P(3)[/tex]
This gives:
[tex]P(x\le 3) = 0.30 + 0.25 + 0.20[/tex]
[tex]P(x\le 3) = 0.75[/tex]
Solving (b): Probability of at most 3 CDs
Here, we consider:
[tex]\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x\le 3) = P(1) + P(2) + P(3)[/tex]
This gives:
[tex]P(x\le 3) = 0.30 + 0.25 + 0.20[/tex]
[tex]P(x\le 3) = 0.75[/tex]
(b) is the same as (a)
Solving (c): Probability of 5 or more CDs
Here, we consider:
[tex]\begin{array}{ccc}{CDs} & {5} & {6\ or\ more}\ \\ {Prob} & {0.05} & {0.05}\ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x \ge 5) = P(5) + P(6\ or\ more)[/tex]
This gives:
[tex]P(x\ge 5) = 0.05 + 0.05[/tex]
[tex]P(x \ge 5) = 0.10[/tex]
Solving (d): Probability of 1 or 2 CDs
Here, we consider:
[tex]\begin{array}{ccc}{CDs} & {1} & {2} \ \\ {Prob} & {0.30} & {0.25} \ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x = 1\ or\ 2) = P(1) + P(2)[/tex]
This gives:
[tex]P(x = 1\ or\ 2) = 0.30 + 0.25[/tex]
[tex]P(x = 1\ or\ 2) = 0.55[/tex]
Solving (e): Probability of more than 2 CDs
Here, we consider:
[tex]\begin{array}{ccccc}{CDs} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x > 2) = P(3) + P(4) + P(5) + P(6\ or\ more)[/tex]
This gives:
[tex]P(x > 2) = 0.20+ 0.15 + 0.05 + 0.05[/tex]
[tex]P(x > 2) = 0.45[/tex]
Drag each equation to show if it could be a correct first step to solving the equation 3(6+x)=24.
ANSWER FAST PLEASE
Answer:
x=2
Step-by-step explanation:
Solve for x.
x² = 9
x=±3
x=±4.5
x=±18
x=±81
Espaol
A math class has 7 girls and 3 boys in the seventh grade and 4 girls and 4 boys in the eighth grade. The teacher randomly selects a seventh grader and an
eighth grader from the class for a competition. What is the probability that the students she selects are both girls?
Write your answer as a fraction in simplest form.
M
Answer:
61%
Step-by-step explanation:
7g+3b= 7th grade
4g+4b= 8th grade
70% chance of a girl getting picked from 7th grade
50% chance of a girl getting picked from 8th grade class
11g+7b= both classes
about 61% chance for both classes to be a girl picked?
your height is 5ft 2 in btw i will give brainliest
Answer:
about 6
Step-by-step explanation:
a shadow is long so it kind of depends on where the sun is but what the shadow is casting off of is no actually that tall
Help me please, Due now.
find the sum of the fractions below 2 1 over 2 + 2 1 over 3
Answer:
[tex] \frac{105}{6} [/tex]
Step-by-step explanation:
[tex] \frac{21}{2} + \frac{21}{3} [/tex]
lowest common multiple of 2 and 3 is 6
21×3 = 63
21×2= 42
they are now going to have the same denominator of 6
[tex] \frac{63}{6} + \frac{42}{6} [/tex]
now u are just gonna add the neumerators and keep the denominator
[tex] \frac{105}{6} [/tex]
Which type of triangle is formed given the following angle measurements?
Angle 1: 50 degrees
Angle 2: 110 degrees
Angle 3: 20 degrees
Which expression has the same value as -4(5 - x)?
A. -4.5 + 4.x
B. -4.5 - 4.x
C. (-4 + 5).(-4 + ( - x))
D. (4 - 5)(-4 - x)
24 divided by 2 times 5 then square foot of it
Answer:
7.75
Step-by-step explanation:
sq rt of (24/2)(5) = sq rt of 60 = 7.75
Answer:
7.75 rounded
Step-by-step explanation:
24 / 2 = 12
12 * 5 = 60
7.7459
rounded its 7.75
ASAP PLS HELP MARKING BRAINLIEST WITH POINTS PLSSSS