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
KatRina [158]
3 years ago
8

In a football or soccer game, you have 22 players, from both teams, in the field. what is the probability of having at least any

two players with the same birthdays? (just assume 365 days a year and don't have to do the exact calendar month and day, use the day number from 1 to 365)
Mathematics
1 answer:
Tamiku [17]3 years ago
8 0

We can solve this problem using complementary events. Two events are said to be complementary if one negates the other, i.e. E and F are complementary if

E \cap F = \emptyset,\quad E \cup F = \Omega

where \Omega is the whole sample space.

This implies that

P(E) + P(F) = P(\Omega)=1 \implies P(E) = 1-P(F)

So, let's compute the probability that all 22 footballer were born on different days.

The first footballer can be born on any day, since we have no restrictions so far. Since we're using numbers from 1 to 365 to represent days, let's say that the first footballer was born on the day d_1.

The second footballer can be born on any other day, so he has 364 possible birthdays:

d_2 \in \{1,2,3,\ldots 365\} \setminus \{d_1\}

the probability for the first two footballers to be born on two different days is thus

1 \cdot \dfrac{364}{365} = \dfrac{364}{365}

Similarly, the third footballer can be born on any day, except d_1 and d_2:

d_3 \in \{1,2,3,\ldots 365\} \setminus \{d_1,d_2\}

so, the probability for the first three footballers to be born on three different days is

1 \cdot \dfrac{364}{365} \cdot \dfrac{363}{365}

And so on. With each new footballer we include, we have less and less options out of the 365 days, since more and more days will be already occupied by another footballer, and we can't have two players born on the same day.

The probability of all 22 footballers being born on 22 different days is thus

\dfrac{364\cdot 363 \cdot \ldots \cdot (365-21)}{365^{21}}

So, the probability that at least two footballers are born on the same day is

1-\dfrac{364\cdot 363 \cdot \ldots \cdot (365-21)}{365^{21}}

since the two events are complementary.

You might be interested in
Pls help WILL MARK BRAINLY also 34 POINTS
Licemer1 [7]

Answer:

X is 38, y is 27.

Step-by-step explanation:

This is because you are subtracting on the 90 degree angles.

4 0
2 years ago
Read 2 more answers
Two cylinders have the same size base, but one is twice as tall. Explain why the taller cylinder does not have double the surfac
Igoryamba

Answer:

The surface area of a cylinder is the sum of the areas of the two bases and the area of the lateral surface. If the height of the cylinder is doubled, the area of the lateral surface is doubled, but the areas of the bases remain the same.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
if you have 48 apples and you gave your friend molly 20 and you gave your brother and mom 18 each how much apples do you have no
Lelechka [254]

Answer:

10

Step-by-step explanation:

48-20=28

28-18=10

that is how I see it at least

6 0
2 years ago
What’s the answer to<br> cos-1(168/240)
Nezavi [6.7K]

Answer:

ans= 45.6

Step-by-step explanation:

I think the ans is 45.6

I hope it will help u...

7 0
3 years ago
What the percent change from 50; 35
il63 [147K]
50 -> 35=change by 15
change by 5=10%
so multiply by 3 
3(5)=3(10%)
15=30%
5 0
3 years ago
Other questions:
  • a rectanguler prism is 7 meters wide,8 meters tall,and 39.5 meters long. what is the volume of the container?
    12·1 answer
  • Need help pls guys I will love you ❤️
    14·1 answer
  • Franco freezes the vegetables he grows in the summer so he can eat them all year long. He packs the vegetables into cube-shaped
    10·1 answer
  • Freddy is two years old than her brother. Twelve years ago, she was twice as old as he was. How old were they? Equation
    9·1 answer
  • Why does one has a line with arrows and the other doesn’t?
    10·1 answer
  • Angela’s and Ben’s Cell Phone Plan
    5·1 answer
  • Amanda Gorman already has plans to run for President. The expression that gives the year in which she hopes to do this is given
    5·1 answer
  • What is 5% of $150 dollars?
    6·2 answers
  • The volume of a cube, in cubic centimeters, is given by the function V(x) = x3, where x is the side length of the cube in centim
    10·1 answer
  • X-23 / x^2 -x- 20 - 2/5-x
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!