1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Masja [62]
3 years ago
13

A football team consists of 20 each freshmen and sophomores, 15 juniors and 10 seniors. Four players are selected at random to s

erve as captains. Find the probability that :
a) all four are seniors
b) There is one each: freshman, sophomore, junior and senior.
c) There are 2 sopomores and 2 fresjhman
d) At least one of the students is a senior
Mathematics
1 answer:
Veronika [31]3 years ago
7 0

Answer:

a)Probability that all four are seniors is 0.0003102

b)Probability of getting one each is 0.00369

c)Probability of picking 2 sophomores and 2 freshers is 0.00889

d)Probability of at least one senior is .4963

Step-by-step explanation:

total  no persons = summing up the no of people present, that is, 20+20+10+15= 65

a) Probability that all four are seniors is given by Pr( all seniors)

Pr(all seniors) =

?\frac{10}[65}*\frac{9}{64}*\frac{8}{63}*\frac{7}{62} =0.0003102

The probability of an event is defined to be the ratio of the number of cases favorable to the event to the total number of cases

 The event in question is mutually dependent in that each event depends on the former

You would notice that the total no of people were reducing with each selection. That means that taking out one senior reduced the total no of students as well as the events

b)  Probability of getting one each = Pr(1 senior)*Pr(1 sophomore)*Pr(1 freshman)*Pr(1 junior)

Pr(1 senior) = 10/64

Pr(1 junior)= 15/63

Pr(1 sophomore) = 20/62

Pr (1 freshman) = 20/61

Therefore pr(1 each)= frac{10}[65}*\frac{15}{64}*\frac{20}{63}*\frac{20}{62} =0.00369

Same explanation in a applies

C) Probability of picking 2 sophomores and 2 freshers = Pr(1 sophmore)*Pr( 2nd sophmore)*Pr(1 fresher)*Pr ( 2nd fresher)

Pr(1 sophmore)= 20/64

Pr ( 2nd sophmore)=19/63

Pr ( 1 fresher)=20/64

Pr ( 2nd fresher)=19/64

Pr(2 sophomores and freshers) = frac{20}[65}*\frac{19}{64}*\frac{20}{63}*\frac{19}{62} =0.00889

d) Probability of at least one senior = 1- Probability(no senior)

No of players without the seniors = 55

Pr(no senior) = probability of choosing 4 out of 55 people divided by the probability of choosing 5 out of 65= 55C4/65C4 =0.5037

Where C means combination

Therefore probability of atleast one senior = 1- .5037= .4963

You might be interested in
If x= 4 and y=5<br> Find the value of x² + 4y 5​
Sati [7]

Answer:

32

Step-by-step explanation:

x^2 + 4y = 16 + 20 = 32

Just do substitution.

Hope this helps.

Good Luck

3 0
3 years ago
Read 2 more answers
Perimeters and Areas of Rectangles (PLEASE HELP)
Lynna [10]

Answer:

i will only answer 11 and 4

Step-by-step explanation:

4: 23 i know its not the whole thing

11:45 its not the full thing

6 0
2 years ago
Read 2 more answers
Use the Euclidean Algorithm to compute the greatest common divisors indicated. (a) gcd(20, 12) (b) gcd(100, 36) (c) gcd(207, 496
coldgirl [10]

Answer:

(a) gcd(20, 12)=4

(b) gcd(100, 36)=4

(c) gcd(496,207 )=1

Step-by-step explanation:

The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.

The Euclidean algorithm solves the problem:

<em>                                   Given integers </em>a, b<em>, find </em>d=gcd(a,b)<em />

Here is an outline of the steps:

  1. Let a=x, b=y.
  2. Given x, y, use the division algorithm to write x=yq+r.
  3. If r=0, stop and output y; this is the gcd of a, b.
  4. If r\neq 0, replace (x,y) by (y,r). Go to step 2.

The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.

Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:

Step 1: Subtract D from N repeatedly.

Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.

(a) To find gcd(20, 12) we apply the Euclidean algorithm:

20 = 12\cdot 1 + 8\\ 12 = 8\cdot 1 + 4\\ 8 = 4\cdot 2 + 0

The process stops since we reached 0, and we obtain gcd(20, 12)=4.

(b) To find gcd(100, 36) we apply the Euclidean algorithm:

100 = 36\cdot 2 + 28\\ 36 = 28\cdot1 + 8\\ 28 = 8\cdot 3 + 4\\ 8 = 4\cdot 2 + 0

The process stops since we reached 0, and we obtain gcd(100, 36)=4.

(c) To find gcd(496,207 ) we apply the Euclidean algorithm:

496 = 207\cdot 2 + 82\\ 207 = 82\cdot 2 + 43\\ 82 = 43\cdot 1 + 39\\ 43 = 39\cdot 1 + 4\\ 39 = 4\cdot 9 + 3\\ 4 = 3\cdot 1 + 1\\ 3 = 1\cdot 3 + 0

The process stops since we reached 0, and we obtain gcd(496,207 )=1.

3 0
3 years ago
BE is a midsegment, Find the value of x. Please
Scrat [10]

Answer:

x10

Step-by-step explanation:

BE=1/2 * CD

x=CB/2

x=20/2

x=10

8 0
2 years ago
Guys help please I am struggling
alina1380 [7]

9514 1404 393

Answer:

  14.1 years

Step-by-step explanation:

Use the compound interest formula and solve for t. Logarithms are involved.

  A = P(1 +r/n)^(nt)

amount when P is invested for t years at annual rate r compounded n times per year.

Using the given values, we have ...

  13060 = 8800(1 +0.028/365)^(365t)

  13060/8800 = (1 +0.028/365)^(365t) . . . . divide by P=8800

Now we take logarithms to make this a linear equation.

  log(13060/8800) = (365t)log(1 +0.028/365)

Dividing by the coefficient of t gives us ...

  t = log(13060/8800)/(365·log(1 +0.028/365)) ≈ 0.171461/0.0121598

  t ≈ 14.1

It would take about 14.1 years for the value to reach $13,060.

8 0
3 years ago
Other questions:
  • Select the correct answer from the drop-down menu find the surface area of this triangular prism
    12·1 answer
  • One month,ruby worked 6 hours more than Isaac, and Svetlana worked 4 times as many hours as ruby. Together they worked 126 hours
    12·1 answer
  • What is the midpoint of the segment shown below?
    8·2 answers
  • John can create 3 apps in 6 weeks while Ben can do the same job in 2 weeks. How many weeks would it take them to create 10 apps
    6·1 answer
  • In a group of people, some are in favor of a tax increase on rich people to reduce the federal deficit and others are against it
    7·1 answer
  • What is the area of this figure?<br><br> Enter your answer as a decimal.
    15·2 answers
  • David just accepted a job at a new company where he will make an annual salary of $69000. David was told that for each year he s
    14·2 answers
  • What is the value of 3-2
    6·1 answer
  • The weight of Jacob’s backpack is made up of the weight of the contents of the backpack as well as the weight of the backpack
    9·1 answer
  • find the surface area a planet if its circumference is about 18,000 miles long. Round to the nearest thousand square miles
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!