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
erastova [34]
2 years ago
8

What is the probability that two people chosen at random were born on the same day of the week? b)What is the probability that i

n a group of n people chosen at random, there are at least two born on the same day of the week? c)How many people chosen at random are needed to make the probability greater than 1/2 that there are at least two people born on the same day of the week?
Mathematics
1 answer:
zaharov [31]2 years ago
7 0

Answer:

See explanation below

Step-by-step explanation:

First, in order to solve this, we need to use the expression to calculate the probability of these events to happen.

The first is conditional probability which is:

P(B|A) = P(AUB)/P(A)

The second would be the complemental rule of probability which is:

P(E) = 1 - P(e)

With these two expressions, let's calculate the probability for each part:

a) A week has 7 days, and for the first person, he has 7 options to be born, so probability of that person is:

P(1st person) = 7/7 = 1

Now, the second person also has the same options than person 1, but the condition here is that he has to match the same day of person 1, so, he only has 1 option out of 7 to be the same day so:

P(A|B) = 1/7

Finally the probability would be:

P = 1 * 1/7 = 1/7 or 0.143

b) In this part, we have a n group of selected random people. Let's use logic here, if we choose more than 8 persons randomly, we know that 2 of them has born on the same day at least. (Think about it, 7 days a week, 7 persons born in different days, but if you add one, that person born one day that another person in the previous group born too), so probability that when n is >7, is 1.

To know that at least 2 person born on the same day of the week, we have to choose a number of 7 people at least. From that number and below, we can calculate the probability. To do this shorter, I will do for n = 7 and n = 6.

By complemental rule, we know that:

P(born on same day) = 1 - P(not born on same day)

The probability of not born on the same day would be n - 1/n° days

For n = 7

We have 7 ways of choosing the first person, 6 ways to choose the seconds, then 5 ways to choose the following and so on....

P = 1 - 7/7 * 6/7 * 5/7 * 4/7 * 3/7 * 2/7 * 1/7 = 0.994

Doing the same thing with n = 6

P = 1 - 7/7 * 6/7 * 5/7 * 4/7 * 3/7 * 2/7 = 0.957

We can do this with n = 5 through n = 3, and you will get the other results if you need to show that.

n = 5

P = 1 - 7/7 * 6/7 * 5/7 * 4/7 * 3/7 = 0.85

n = 4

P = 1 - 7/7 * 6/7 * 5/7 * 4/7 = 0.65

n = 3

P = 7/7 * 6/7 * 5/7 = 0.388

c) As you can see, in the part b) when the value of n is 4 or higher, you'll get a probability greater than 1/2 (0.5), so we need to choose at least 4 people at random.

c)

You might be interested in
The temperature started at 82° and continued to rise at a rate of 0.6° each hour the temperature is now 85° determine the number
Gnesinka [82]

Answer:

5 hours

Step-by-step explanation:

Our goal here is 3 F because 82+3=85

Ok so you start at 82. For example, you can do 0.6×1=0.6 (no)

0.6×2=1.2 (no)

0.6×3=1.8 (no)

0.6×4=2.4 (no)

0.6×5=3 (yes)

82°+3°=85°

8 0
3 years ago
It says it in the image please help me
r-ruslan [8.4K]

Answer:

The answer you have selected should be correct.

6 0
2 years ago
In a box and whisker plot, can the upper quartile also be the greatest value? Explain
Luda [366]

Answer:

No

Step-by-step explanation:

The upper Quartile is also known as the third quartile. And the greatest value is at the far right of the plot I placed an image below

3 0
3 years ago
Please help, see image
ZanzabumX [31]

Answer:

it block pic

Step-by-step explanation:

5 0
3 years ago
If the perimeter of an equilateral triangle is 36 inches what is the perimeter of it’s image under a dilation with a scale facto
alexdok [17]

Answer:

The perimeter of the image is 144 inches

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

The perimeter of the image is equal to the perimeter of the pre-image multiplied by the scale factor

36(4)=144\ inches

6 0
3 years ago
Other questions:
  • The answer, asap!!!
    5·1 answer
  • The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.
    11·2 answers
  • Avery has a total of $12.50 in her piggy bank at home. Each week she takes out $1.25 to ride the city bus. Write an equation rep
    10·1 answer
  • K divide by 6 + 8 = 5
    14·1 answer
  • 15 POINTS HELP ME PLEASE!!!
    7·2 answers
  • Factor <br> 2x^2-5x+3<br> need help
    6·2 answers
  • Solve the inequality.<br> - 6 &lt; 2x - 4 &lt;4
    14·1 answer
  • PLEASE ANSWER ASAP!! pic attached. will mark brain list IF you’re correct
    10·2 answers
  • 4k^2 + 28k + 48 factor the polynomial​
    14·1 answer
  • PLSSS HELLPP MEEEEE!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!