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
viva [34]
3 years ago
5

Approximately 80,000 marriages took place in the state of New York last year. Estimate the probabilitythat for at least one of t

hese couples,(a) both partners were born on April 30;(b) both partners celebrated their birthday on the same day of the year.State your assumptions.
Mathematics
1 answer:
lilavasa [31]3 years ago
7 0

Answer:

a. 0.45 b. 1

Step-by-step explanation:

We will be using Poisson Approximation of Binomial because n = 80,000 is large and probability (<em>p) </em>is very small.

We calculate for (a) as follows:

The probability that both partners were born on April 30 is

<em>p </em>= 1/365 X 1/365

<em>p </em>= 1/133,225

<em>p </em>= 0.00000751

Using Poisson Approximation, we have:

λ = n<em>p</em>

λ = 80,000 X 0.00000751

λ = 0.6

We use λ to calculate thus:

P (X \geq 1) = 1 - P ( X = 0)

              = 1 - e^-λ

              = 1 - e^-0.6

              = 0.451

There is a 45.1% probability that, for at least one of these couples, both partners were born on April 30.

(b) To calculate the probability that both partners celebrated their birthday on the same day:

<em>p </em>(same birthday) = 365 X 1/365 X 1/365

                             = 1/365

λ = n<em>p</em>

λ = 80,000 X 1/365

λ = 219.17

P (X \geq 1) = 1 - P ( X = 0)

= 1 - e^-λ

= 1 - e^-219.17

≈ 1

There is almost 100% probability that, for at least one of these couples, both partners celebrate their birthday on the same day of the year.

You might be interested in
Martha and Janet each decide to invest $600 into different accounts. Martha's account earns $4.50 every month. Janet's account e
ehidna [41]

Answer:

<u>Janet's interest is $3.90 every month.</u>

Step-by-step explanation:

First, you need to set up a proportion to find Janet's interest:

0.65%/100 = x/600

Step 1: Cross-multiply.

0.65/100/100 = x/600

(0.65/100)*(600)=x*(100)

39/10=100x

Step 2: Flip the equation.

100x=39/10

Step 3: Divide both sides by 100.

100x/100=39/10/100

x=39/1000 (0.039)

Then move the decimal twice to the left to find the dollar amount:

0.039 ⇒ 3.90

Janet's interest is $3.90 every month.

HOPE THIS HELPS!!! <33333

-Silver

5 0
3 years ago
Read 2 more answers
The answer?????????????
Aleksandr-060686 [28]

Hey there!

In a rhombus, opposite angles are congruent. This means that 2y is equal to y+34. Let's set up an equation to solve for y.

2y=y+34

We subtract y from both sides.

y=34

Therefore, y=34°

I hope that this helps! Have a wonderful day!

6 0
3 years ago
3 – (–3) + 7 – 4 =
Zanzabum

Answer:

=9

Step-by-step explanation:

3–(–3)+7–4=

=3+3+7-4

=6+7-4

=13-4

=9

I hope this helps!

8 0
3 years ago
Read 2 more answers
How do you name a triangle
salantis [7]
The labels of the vertices of the triangle<span>, which are generally capital letters, are used to </span>name a triangle<span>. </span>
8 0
3 years ago
Read 2 more answers
how many pairs of opposite sides are parallel in a trapezoid? how is this different from a parallelogram?
elena-s [515]

Answer:

one pair of parallel sides.

Step-by-step explanation:

A trapezoid has just one pair of sides parallel.

The parallel sides if a trapezoid forms its base.

A parallelogram on the other hand, has two pairs of sides parallel.

The pair of parallel sides in the trapezoid are not congruent while the pair of parallel sides in a parallelogram are congruent.

8 0
3 years ago
Other questions:
  • 35% of a number is 17. Work out the number.
    13·1 answer
  • Which equation yields the solutions x=−2 and x=5?
    15·2 answers
  • A person is to install five devices each 6 7/8 inches wide with 3 1/2 inches between switches. How much space will be needed to
    11·1 answer
  • Find the area of the shaded region.
    13·1 answer
  • Which graph does not represent y as a function of x
    10·1 answer
  • The perimeter of a rectangular is 86 m. If the width were doubled and the length were increased by 22 m, the perimeter would be
    5·1 answer
  • Kay scored above 90% on five of her math quizzes, 80% to 90% on fourteen of them, and 70% to 80% on two of them. What is the exp
    10·1 answer
  • Rachel has twice as much money as Paul. If I gave Rachel $250, she will then have three times as much as Paul. How much did each
    5·2 answers
  • PLS HELP 96POINTS Which statement is true for light passing into a medium that is more optically dense than the first medium thr
    5·2 answers
  • Liam is a tyre fitter.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!