PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!

Baseball's division series is a best of five game series. That is, the first team to win 3 games is the winner. Team A and team

iris [78.8K]

Answer:

1. 27.46% probability that A wins the series in 3 games.

2. There is a 28.84% probability A wins the series in 4 games.

3. There is a 20.18% probability A wins the series in 5 games.

4. There is a 76.48% probability A wins the series.

5. There is a 71.825% probability A wins the series if a "best-of-three" game series is played.

Step-by-step explanation:

For each game, there are these following probabilities:

A 65% probability team A wins.

A 35% probability team B wins.

The combination formula is important to solve this problem:

This is because for example, team A winning games 1,2 and 4 and team B winning game 3 is the same as team A winning games 1,3,4 and team B winning game 2. That is, the order is not important.

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

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

1. What the probability that A wins the series in 3 games?

This is team A winning all 3 games. For each game, there is a 65% probability that team A wins. So

$P = (0.65)^{3} = 0.2746$

There is a 27.46% probability that A wins the series in 3 games.

2. What is the probability A wins the series in 4 games?

This is the team A winning three games and the team B 1. The team B win cannot happen in the fourth game, so the number of possibilities is a combination of 3 by 2. So

$C_{3,2} = \frac{3!}{2!1!} = 3$

The probability that team A wins the series in 4 games is:

$P = 3*(0.65)^{3}*(0.35) = 0.2884$

There is a 28.84% probability A wins the series in 4 games.

3.What is the probability A wins the series in 5 games?

This is the team A winning three games and the team B 2. The team B second win cannot happen in the fifth game, so the number of possibilities is a combination of 4 by 2. So

$C_{4,2} = \frac{3!}{2!1!} = 6$

The probability that team A wins the series in 5 games is:

$P = 6*(0.65)^{3}*(0.35)^{2} = 0.2018$

There is a 20.18% probability A wins the series in 5 games.

4. What is the probability A wins the series (period)?

They can win the series in 3,4 or 5 games. So this is the sum of the answers for 1,2,3.

So

$P = 0.2746 + 0.2884 + 0.2018 = 0.7648$

There is a 76.48% probability A wins the series.

5. What is the probability A wins the series if a "best-of-three" game series is played?

These three following outcomes are accepted:

A - A

A - B - A

B - A - A

So

$P = (0.65)^{2} + 2*(0.65)^{2}*(0.35) = 0.71825$

There is a 71.825% probability A wins the series if a "best-of-three" game series is played.

3 0

3 years ago

2. Solve the system of equations using the substitution method.

Dimas [21]

Answer:

x = 1

Step-by-step explanation:

2x + 3y = 20

2x + 3(10-4x) = 20

2x + 30 - 12x = 20

combine like terms

-10x + 30 = 20

-30 -30

-10x = -10

divide both sides by -10

x = 1

Hope this Helps!!!

7 0

3 years ago

120-2x=30, what’s x?

KiRa [710]

Step-by-step explanation:

-2x=30-120

-2x = -90

=x = -90/-2

=x = +45

4 0

4 years ago

What is the value of k? <br> -k+78=98-20

Jlenok [28]

Answer:

k=0

Step-by-step explanation:

6 0

3 years ago

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term $x^2$ , which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression: $x_v=\frac{-b}{2a}$

Since in our case $a=1$ and $b=5$ , we get that the x-position of the vertex is: $x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

$y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}$

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the $x_v=-\frac{5}{2}$ . Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

$f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0$

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0

3 years ago