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
Aleksandr [31]
2 years ago
5

. Imagine a game of 3 players where exactly one player wins in the end and all players have equal chances of being the winner. T

he game is repeated four times. Find the probability that there is at least one person who wins no games. Hint: Consider the events Ai in which person i wins no games and use the inclusion-exclusion formula.
Mathematics
1 answer:
lbvjy [14]2 years ago
6 0

Answer:

5/9

Step-by-step explanation:

Number of players = 3

number of times game is repeated = 4

P( any person wins a game ) = 1/3

P ( any person does not win a game ) = 1 - 1/3 = 2/3

P ( any person wins no game in 4 attempts ) = ( 2/3 )^4 = 16/81

<em>Note : each player has equal chance of winning </em>

<u>Find the probability that there is at least one person who wins no games </u>

lets represent the probability of each player not wining a game with alphabet A

A1 = player 1 wins no game

A2 = player 2 wins no game

A3 = players 3 wins no game

Applying the inclusion-exclusion formula

<em>P( A1 ∪ A2 U A3 )</em><em> = P(A1 ) + P(A2) + P(A3) - P( A1 ∩ A2 ) - P( A2 ∩ A3 ) - P( A1            ∩ A3 )  + P( A1 ∩ A2 ∩ A3 ) </em>

where

P( A1 ∩ A2 ) = P( A1 wins all games )

P ( A1 wins all games in 4 attempts ) = ( 1/3 )^4 = 1/81

P( A1 ∩ A2 ∩ A3 ) = P ( no players wins any game in 4 attempts ) = 0

Hence

P( A1 ∪ A2 U A3 ) = 16/81 + 16/81 + 16/81 - 1/81 - 1/81 - 1/81 - 0 = 5/9

You might be interested in
A bathtub can hold 80 gallons of water. The faucet flows at a rate of 4 gallons per minute. What percentage of the tub will be f
Talja [164]
30 percent will be filled I am positive that is it
8 0
2 years ago
Read 2 more answers
(100 points) find the cost of each treat
Anna71 [15]

Answer:

icecream = $2.99

donut = $1.19

creamcake = $4.99

Step-by-step explanation:

The picture shows $7.17 for 2 x ice-cream and 1 donut

We are given 3 cream cakes that total 14.97 we divide by 3 = 4.99

9.17- 4.99=4.18

=5.37-4.18 =1.19

we can then fill out the boxes.

1.19 +1.19 = 2.38 = 5.37-2.38= £2.99

2.99 +2.99 +1.19 = $7.17

We can see total first two rows = $12.56

2.99+2.99+2.99 +1.19 +1.19+1.19 = $12.56

4 0
3 years ago
Read 2 more answers
What’s 7y+8=57?????!!?!????
forsale [732]
Ok so basically your going to subtract 57-8 which is 49. So now you have 7y=49 so now divide 49 by 7 which is 7. So your answer is 7 and to check your work substitute 7 for y so.... 7(7)+8=57 so 57=57 which is accurate
7 0
3 years ago
Read 2 more answers
10% of Kindergarteners know how to read before school starts. If there are 150 kindergarteners at a
Tamiku [17]

Answer:

15

Step-by-step explanation:

To get 10 percent, you divide by 10.

150 divided by 10 equals 15.

3 0
3 years ago
Read 2 more answers
Last week f40 fifth graders went on a field trip to the science museum
Xelga [282]
8 out of 40 fifth graders went to see the lab animal presentation. This can be written as this expression:

\frac{8}{40}

Find the greatest common factor of 8 and 40:

Factors of 8: 1, 2, 4, 8
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

Therefore the greatest common factor is 8. Divide both the numerator and the denominator by 8.

\frac{8}{40} = \frac{8/8}{40/8} = \frac{1}{5}

Therefore the fractional part is \frac{1}{5}.

To get the percentage, you need to get the denominator to a value of 100.

To do so, you need to find the value to multiply both the numerator and denominator by to achieve this.

To get this value, you can divide 100 by the denominator of the fractional value.

100 / 5 = 20

Then you can multiply both the numerator and denominator by 20:

\frac{1}{5} = \frac{1 * 20}{5 * 20} = \frac{20}{100}

From here, the numerator will state the percentage:

20\%

Hope this helps :)


8 0
3 years ago
Read 2 more answers
Other questions:
  • Solve the equation 5x + 7y = 35 for y
    15·2 answers
  • If a cookie weighs
    6·2 answers
  • Can somebody help me with this it a little hard
    5·1 answer
  • Verbal expression for 1/8y
    13·1 answer
  • How to write 16,208.59 in word form
    12·1 answer
  • Which of the following functions is a direct variation?
    9·1 answer
  • MICHAEL and Kevin are running. Kevin gets a 3 mile head start and runs at a rate of 5.5 miles per hour.  Michael runs at a rate
    8·1 answer
  • A model rocket is launched from a platform 12 meters high at a speed of 35 meters per second. Its height h can be modeled by the
    11·1 answer
  • Solve for m 4=m+4 :) what does m = ?
    10·1 answer
  • What shape is this called in mathematical term​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!