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Anna007 [38]
3 years ago
12

On each round, Ann and Bob each simultaneously toss a fair coin. Let Xn be the number of heads tossed in the 2n flips which occu

r during the first n rounds. For each integer m > 0, let rm denote the probability that there exists an n such that Xn = m.
Mathematics
1 answer:
CaHeK987 [17]3 years ago
8 0

Answer:

P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}

Step-by-step explanation:

In a coin toss the  probability of tossing a head is 0.5 (50% head/50% tails)

If n is the number of rounds and 2n the number of coins tossed (one for each player), the probability of having m heads tossed is:

R=\frac{2n!}{m!*(2n-m)!}

R is the number of cases (combination of coins tossed) that gives a m number of heads. Each case has a probability of P_{case}=0.5^{2n} so:

P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}

<u>For example, to toss 4 heads in 5 rounds: </u>

  • n=5
  • 2n=10
  • m=4

P=\frac{10!}{4!*(10-4)!}*0.5^{10}

P=\frac{10*9*8*7*6!}{4!*6!}*0.5^{10}

P=\frac{10*9*8*7}{4!}*0.5^{10}

P=\frac{10*9*8*7}{4!}*0.5^{10}=0.205

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How many times greater is the volume of the large bowl than the volume of the small bowl
arsen [322]
Answer: it depends on how big each bowl could be. depending on how big the diameter of the bowl is, we can figure out what the radius is, and then we could multiply that by pi squared, which gets you the area of the circle. Then we could figure out how much larger the large bowl is than the smaller bowl with the diameter knowledge that we gained.

So, for example, there was a bowl like this: (|||) (imagine that is a full circle) and that would be... about 9 in. across. imagine the smaller bowl is about 3in. across. then, we could figure out the radius by finding the middle, and expand the middle to the edge of the bowl. then, whatever the radius is, we could multiply that by 8, and get the total diameter of the bowl in inches. with that knowledge, we should be able to know the area of the bowl, by getting the diameter, and multiplying it by pi squared which equals 9.42, and then you multiply that by the radius and the diameter to get the area of the bowl.


that is how you could figure out how much bigger the large bowl is than the smaller bowl.
4 0
4 years ago
Please someone help me
Digiron [165]
26*19=494.
480-494=-14
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4 0
3 years ago
it takes maya 30 minutes to solve 5 logic puzzles,and it takes amy 28 minutes to solve 4 logic puzzles, in minutes per puzzle
Harman [31]

Answer:

MAYA (6 minutes)

Amy (7 minutes)

Step-by-step explanation:

MAYA

Takes Maya 30 minutes to solve 5 Puzzle:

Let's express it as,

30 mins = 5 Puzzle

1 min = x Puzzle

Cross multiply to solve for the number of questions Maya solves in a minute.

It becomes:

30*x = 5*1

30x = 5

x = 30/5

x = 6mins.

It means it takes Maya 6 mins to solve one question.

FOR AMY

Takes Amy 28 mins to solve 4 puzzles.

Let's represent it as:

28 mins = 4 Puzzles

x min = 1 puzzle

Let's solve for x

(28 mins) * (1 puzzle) = 4 * x

28 = 4x

x = 28/4

x = 7 mins

It means, it takes Amy 7 minutes to solve 1 puzzle

4 0
3 years ago
Write an equation in slope-intercept form of the line that passes through (2,0) and is perpendicular to y=1/5 x-2.
Advocard [28]

Answer:

y = -5x+10

Step-by-step explanation:

Given

(x_1,y_1) = (2,0)

y = \frac{1}{5}x - 2

Required

Determine an equation that perpendicular to the equation

An equation has the form:

y = mx + b

Where

m = slope

By comparison:

m = \frac{1}{5}

Next, we determine the slope of the new line.

When two lines are perpendicular, the following relation exist:

m_2= -\frac{1}{m_1}

Substitute 1/5 for m1

m_2= -\frac{1}{1/5}

m_2= -5

The equation of the line is then calculated using:

y - y_1 = m(x - x_1)

Where:

m_2= -5 and (x_1,y_1) = (2,0)

This gives:

y - 0 = -5(x - 2)

y = -5(x - 2)

y = -5x+10

8 0
3 years ago
What is 5X minus Y equals six minus 2X plus Y equals eight
34kurt

Answer:

x = 8/3, y = 22/3

Step-by-step explanation:

5x-y=6-2x+y=8

5x-y=8 --- 1

6-2x+y=8 --- 2

by solving 1 and 2, x = 8/3, y = 22/3

5 0
3 years ago
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