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
Katyanochek1 [597]
3 years ago
11

Dawn comma Sergio comma Tyrone comma and Jim have all been invited to a dinner party. They arrive randomly and each person arriv

es at a different time. a. In how many ways can they​ arrive? b. In how many ways can Dawn arrive first and Jim ​last? c. Find the probability that Dawn will arrive first and Jim last.
Mathematics
1 answer:
professor190 [17]3 years ago
3 0

Answer:

a. 24

b. 2

c. 0.0833 = 8.33%

Step-by-step explanation:

a.

The first "slot" of person to arrive has 4 possibilities, then the second "slot" will have 3 possibilities, as one has already arrived, then the third "slot" has 2 possibilities, and the fourth "slot" has just 1 possibility.

So, multiplying all these combinations, we have 4*3*2*1 = 24 possible ways they can arrive

b.

If the first and the last person are already "locked", we just have possibilities for the second and third person. The second will have 2 possibilities (Sergio or Tyrone), and the third will have only 1 (the person that wasn't the second between Sergio and Tyrone). So, the number of possibilities is 2*1 = 2

c.

If we have 2 cases where Dawn is first and Jim is last, from a total of 24 possible cases, the probability is 2/24 = 1/12 = 0.0833 = 8.33%

You might be interested in
In a particular faculty 60% of students are men and 40% are women. In a random sample of 50 students what is the probability tha
zimovet [89]

Answer:

a) The expected value is given by:

E(X) = np = 50*0.4 = 20

and the variance is given by:

Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12

b) P(X>25)= 1-P(X\leq 25)

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

P(X>25)= 1-P(X\leq 25)=0.0573

c) 1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

X \sim N(\mu = 20 , \sigma= 3.464)

d) P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z

e) P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)

P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=50, p=0.4)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

The expected value is given by:

E(X) = np = 50*0.4 = 20

and the variance is given by:

Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12

Part b

For this case we want to find this probability:

P(X>25)= 1-P(X\leq 25)

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

P(X>25)= 1-P(X\leq 25)=0.0573

Part c

1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

X \sim N(\mu = 20 , \sigma= 3.464)

Part d

We want this probability:

P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z

Part e

For this case we use the continuity correction and we have this:

P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)

P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z

4 0
3 years ago
heeeelllllpppppp heyyy i need help asap and please try your best and solve the problem out it would be greatly appreciated becau
andreev551 [17]

Answer:

{10}^{ - 14}

Step-by-step explanation:

\huge\frac{ {10}^{ - 9} }{ {10}^{5} }  \\  \\  \huge =  {10}^{ - 9}  \times  {10}^{ - 5}  \\  \\  \huge =  {10}^{ - 9  + ( - 5)}  \\  \\ \huge =  {10}^{ - 9 - 5}  \\  \\  \huge \orange {=  {10}^{ - 14}}

7 0
3 years ago
Read 2 more answers
What is the point-slope form equation of the graph?
sammy [17]

Answer:

y-4= 1/2(x+2)

Step-by-step explanation:

6 0
3 years ago
What is the solution to the system of equations graphed below?
tatiyna

I think it is D..

.

BMK

8 0
2 years ago
-8+(-4)+(-2)+(-1)+(-1/2)+.... what is the sum of the first 7 terms of the geometric series
likoan [24]
Your answer is 15.875

-8+(-4)+(-2)+(-1)+(-1/2)+(-1/4)+(-1/8)
you half the previous vaule to find the next value

8 0
3 years ago
Other questions:
  • Which is the location of S' when trapezoid RSTU is rotated 90° clockwise about the origin to produce trapezoid R'S'T'U? Explain.
    15·1 answer
  • The following polynomial is defined on the interval [-2, 2]:
    10·1 answer
  • A rectangle has an area of 192 square inches. Find it’s length and width if the length is 3 times the width
    5·1 answer
  • Lincoln Middle School plans to collect more than 2000 cans of food in a food drive. So far, 668 cans have been collected. Write
    9·1 answer
  • A committee of 2 people is to be chosen from 5 women and 5 men. What is the probability at least one man was chosen given at lea
    15·2 answers
  • 10×5+4 2 +(5+30÷10) Order Of Operations
    13·1 answer
  • Tan(x-y) if cscx=13/5 and coty=4/3
    10·1 answer
  • Factor the expression -8x 2+ 22x - 15
    9·2 answers
  • Any one know the answer for this question??????
    13·1 answer
  • Lois jumped 270 times in 6 hours. At that rate, how many times would she jump in 4 minutes?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!