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sveta [45]
3 years ago
6

A football team has a probability of .75 of winning when playing any of the other four teams in its conference. If the games are

independent, what is the probability the team wins all its conference games?
Mathematics
1 answer:
Alexeev081 [22]3 years ago
4 0

Answer:

0.3164 = 31.64% probability the team wins all its conference games

Step-by-step explanation:

For each conference game, there are only two possible outcomes. Either the team wins it, or they lose. The probability of winning a game is independent of any other game. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A football team has a probability of .75 of winning when playing any of the other four teams in its conference.

The probability means that p = 0.75, and four games means that n = 4

If the games are independent, what is the probability the team wins all its conference games?

This is P(X = 4). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{4,4}.(0.75)^{4}.(0.25)^{0} = 0.3164

0.3164 = 31.64% probability the team wins all its conference games

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I have a question here. ​
taurus [48]

9514 1404 393

Answer:

  P(F|A) = 35%

Step-by-step explanation:

P(F|A) = P(F&A)/P(A) = 7%/20% = 0.35

P(F|A) = 35%

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The given numbers will let you fill in a table for all of the categories of workers. However, it turns out this question can be answered using only the numbers given in the problem statement.

6 0
2 years ago
Marvin invested 65% of his retirement account in stocks and 35% in gold. Marvin believes that the return to stocks over the next
ser-zykov [4K]

Answer:

1)

the mean rate of return is 17 %

the standard deviation of return is 17.06055

2)

the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325

Step-by-step explanation:

Given the data in the question;

1)

For the portfolio, the mean return and standard deviation are computed as follows;

Mean = Return = 0.65 × 10 + 0.35 × 30

= 6.5 + 10.5

= 17 %

Therefore, the mean rate of return is 17 %

Standard deviation will be;

σp = √( 0.65² × 15² + 0.35² × 40² )

= √( 0.4225 × 225 + 0.1225 × 1600 )

= √( 95.0625 + 196 )  

= √291.0625

= 17.06055  

Therefore, the standard deviation of return is 17.06055

2)  

probability that Marvin's portfolio will make at least 20% over the next 12 months.

P( X > 20 )

we convert to a standard normal variable;

Z = \frac{20-17}{17.06055} )

Z = 0.17

from z table, p-value is;

p( X < 20 ) = 0.5675

P( X > 20 ) 1 - 0.5675  = 0.4325

Therefore, the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325

5 0
3 years ago
What is -0.29 + 1.5​
svp [43]

Answer:

1.21

Step-by-step explanation:

-0.29 + 1.5 = 1.21

5 0
3 years ago
Need help with this problem please
MrMuchimi
I think she bought 23 feet
8 0
3 years ago
Which equation is perpendicular to y = 4x - 6 and passes through point (8, 12).
sergeinik [125]

Answer:

The line is ;

4y = -x + 56

or

y = -x/4 + 14

Step-by-step explanation:

Generally, the equation of a straight line is;

y = mx + c

where m represents the slope

so for y = 4x - 6

The slope is 4

If two lines are perpendicular, the product of their slopes is -1

So for the second line, the slope will be -1/4

The equation in the point slope format will be ;

y-12 = -1/4(x-8)

y-12 = -x/4 + 2

Multiply through by 4

4y-48 = -x + 8

4y = -x + 8 + 48

4y = - x + 56

7 0
3 years ago
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