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djyliett [7]
3 years ago
10

Construct the discrete probability distribution for the random variable described. Express the probabilities as simplified fract

ions. The number of tails in 5 tosses of a coin.
Mathematics
1 answer:
lisov135 [29]3 years ago
5 0

Answer:

P(X = 0) = 0.03125

P(X = 1) = 0.15625

P(X = 2) = 0.3125

P(X = 3) = 0.3125

P(X = 4) = 0.15625

P(X = 5) = 0.03125

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, which 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.

Fair coin:

Equally as likely to be heads or tails, so p = 0.5

5 tosses:

This means that n = 5

Probability distribution:

Probability of each outcome, so:

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

P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125

P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625

P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125

P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125

P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625

P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125

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never [62]

Answer:

P(n>55)=0.1357

Step-by-step explanation:

From the question we are told that:

Sample size n=100

Sample space n'=36

Generally the equation for the mean number of times odds appears is mathematically given by

\=x_o=hp

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Generally the equation for standard deviation is mathematically given by

\sigma=(hp(1-p))^{1/2}\\\sigma=(50(0.5))^{1/2}

\sigma=5

Therefore probability to make wrong decision P(n>55)

P(n>55)=1-P(z55)=1-P(z55)=1-0.86

P(n>55)=0.1357

8 0
3 years ago
How to solve inscribed angles
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Rectangle STUV is shown on a coordinate plane. Rectangle STUV with vertices S at negative 7 comma 6, T at negative 2 comma 6, U
rusak2 [61]

The coordinate of the point T after the given transformations is; T''(-2, -4)

<h3>How to carry out Translation Transformations?</h3>

We are given the coordinates of the rectangle STUV as;

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T(-2, 6)

U(-2, 1)

V(-7, 1)

Now, we are told that all these coordinates are translated using the transformation rule;  (x, y) → (x − 2, y − 4)

Thus, the new coordinates using this transformation rule are;

S'(-9, 2)

T'(-4, 2)

U'(-4, -3)

V'(-9, -3)

Now, we are told that these new points are  rotated 90° counterclockwise and as such the new coordinates formed will follow the pattern (x, y) → (-y, x).

Thus, our final coordinates are;

S''(-2, -9)

T''(-2, -4)

U''(3, -4)

V''(3, -9)

Thus, the coordinate of the point T after the given transformations is; T''(-2, -4)

Read more about Translation Transformation at; brainly.com/question/4289712

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4 0
2 years ago
Read 2 more answers
Help me please i would really appreciate it ill give 20+ points
Alinara [238K]
It might be d because the side are all the exact same size!
6 0
3 years ago
50 POINTS !!<br><br> PLEASE HELP ILL GIVE BRAINLIEST !!
dybincka [34]

Answer:

3.9 miles

Step-by-step explanation:

Use phytagoras theorem

c²=a²+b²

4²=1²+b²

16=1+b²

b²=16-1

b²=15

b=

\sqrt{15}

b= 3.872

≈3.9miles

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