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2 years ago

a fair coin is flipped 10 times. what is the probability of getting the same number of heads and tails

Mathematics

1 answer:

Dafna11 [192]2 years ago

3 0

If you flip a coin one time, the probability to get a Head is

p = 1/2

The probability of not getting a head in a single toss is :

q = 1 - 1/2 = 1/2

Thus there is only one unique situation to get the same number of heads and tails : in 10 toss you need to get exactly five heads, it will means that the rest is the tails.

Now using Binomial theorem of probability, the probability of getting exactly x = 5 heads in a total of n = 10 tosses is :

P(X = 5) = $\frac{10!}{5!*5!} *(\frac{1}{2})^{5} *(\frac{1}{2})^{5}$ ≈ 0.246

So the probability of that is 24,6 %

Good Luck

You might be interested in

-5(x+7)<10. What does x equal?

gulaghasi [49]

Answer:

X>-9

Step-by-step explanation:

Distribute

-5x-35<10

add 35 on both sides

-5x<45

Divide -5 on both sides and flip the sign since your dividing by a NEGATIVE number

x>-9

4 0

3 years ago

Read 2 more answers

A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normal

GenaCL600 [577]

Answer:

A 95% confidence interval for the true mean is [$3.39, $6.01].

Step-by-step explanation:

We are given that a random sample of 10 parking meters in a resort community showed the following incomes for a day;

Incomes (X): $3.60, $4.50, $2.80, $6.30, $2.60, $5.20, $6.75, $4.25, $8.00, $3.00.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean income = $\frac{\sum X}{n}$ = $4.70

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = $1.83

n = sample of parking meters = 10

$\mu$ = population mean

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.262 < $t_9$ < 2.262) = 0.95 {As the critical value of t at 9 degrees of

freedom are -2.262 & 2.262 with P = 2.5%}

P(-2.262 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.262) = 0.95

P( $-2.262 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu$ < $2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.70-2.262 \times {\frac{1.83}{\sqrt{10} } }$ , $4.70+ 2.262 \times {\frac{1.83}{\sqrt{10} } }$ ]

= [$3.39, $6.01]

Therefore, a 95% confidence interval for the true mean is [$3.39, $6.01].

The interpretation of the above result is that we are 95% confident that the true mean will lie between incomes of $3.39 and $6.01.

Also, the margin of error = $2.262 \times {\frac{s}{\sqrt{n} } }$

= $2.262 \times {\frac{1.83}{\sqrt{10} } }$ = 1.31

4 0

3 years ago

What percent is 56 of 200

GrogVix [38]

Answer:

28%

Step-by-step explanation:

7 0

2 years ago

Help!!!! Number 4 right answer

USPshnik [31]

The answer would be 0 solutions.

Here, we see |x+6| = 2.
Oh wow! A foreign object!
|x+6|... two lines... what is that?

That is called absolute value. Whatever is inside the two lines, must have a positive answer!

Let's pretend we have a machine that has this absolute value function activated.
What we put in, we must get a positive answer out.

Let's put in -6.

-6 ==> BEEP BEEP ==> 6

Let's try 3.

3 ==> BEEP BEEP ==>3

Whatever we put in, if it is negative or positive, what comes out is always positive.

So, for how many values x is |x+6|=-2 true?

None, because the answer must be positive!
-2 is not positive, 2 is.

8 0

3 years ago

In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz

BabaBlast [244]

Answer:

C (2, -1)

Step-by-step explanation:

C has the same x coordinate as A = 2

that eliminates A and B.

and the y value of C has to be closer to the y value of B than to the y value of A (due to the 5:3 ratio).

so, without spending unnecessary effort on actual calculation, we can directly derive the correct answer to be C.

but to show in numbers, the "coordinate triangle" of the difference between D and B is a similar triangle to ACD. and so, the ratio of one side pair applies then to all other sides too. including the individual coordinate differences.

so, also the y difference of A to D relates to the y difference between D and B in the same ratio of 5:3 of the overall y difference of A to B.

the y difference A to B is 2 - -6 = 8

the 5/3 split of 8 units is actually 5 and 3.

so, the y coordinate of D is -6 + 5 = -1

and C must have the same y coordinate.

therefore, it is proven that answer C (2, -1) is the right answer.

4 0

2 years ago