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3 years ago

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if a pair of standard dice are rolled what is the probability that one die shows a six but not both of them. reduced fraction an

swer

1 answer:

Novay_Z [31]3 years ago

6 0

Answer:

$P=\frac{5}{18}$

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

so

Let

x------> size of the event space

y-----> size of the sample space

if a die is rolled the sample space is

$\{1,2,3,4,5,6\}$

if two dice rolled the sample space is

$\{1,2,3,4,5,6\}*\{1,2,3,4,5,6\}$

so

The possible pairs are

$y=6*6=36$

The size of the event space x is

$\{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}$

$x=10$

$P=\frac{x}{y}$

substitute

$P=\frac{10}{36}$

Simplify

$P=\frac{5}{18}$

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USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take eight people at random off

Law Incorporation [45]

Answer:

a) Figure and code attached

b) $E(X)=\mu = np = 8*0.2= 1.6$

$Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28$

$Sd(X)=\sigma= \sqrt{1.28}= 1.131$

c) $P(X\geq 7) =0.97$

And we can calculate this with the complement rule.

$P(X \geq 7) = 1-P(X$

So then we have:

$P(X \leq 6) = 0.03$

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=8, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Part a

We can use the following R code to generate the histogram for this case:

> x <- seq(0,8,by = 1)

> y <- dbinom(x,8,0.2)

> plot(x,y,type = "h",main="Histogram")

And as we can see we got the result on the figure attached. And the distribution seems to be skewed to the right.

Part b

For this case the expected value is given by:

$E(X)=\mu = np = 8*0.2= 1.6$

The variance is given by:

$Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28$

And the standard deviation would be:

$Sd(X)=\sigma= \sqrt{1.28}= 1.131$

Part c

For this case we have the following inequality:

$P(X\geq 7) =0.97$

And we can calculate this with the complement rule.

$P(X \geq 7) = 1-P(X$

So then we have:

$P(X \leq 6) = 0.03$

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

5 0

3 years ago

Simplify square root of ten times square root of eight.

Romashka-Z-Leto [24]

<h2>Explanation:</h2><h2></h2>

Here we need to simplify the square root of ten times square root of eight, so let's write this step by step:

Step 1. The square root of ten

$\sqrt{10}$

Step 2. The square root of eight

$\sqrt{8}$

Step 3. The square root of ten times square root of eight

$\sqrt{10}\times \sqrt{8} \\ \\ \\ \text{From radical property:} \\ \\ \sqrt{a}\times \sqrt{b}=\sqrt{ab} \\ \\ \\ So: \\ \\ \sqrt{10}\times \sqrt{8}=\sqrt{80} \\ \\ \\ But: \\ \\ \sqrt{80}=\sqrt{16\time5}=\sqrt{16}\sqrt{5}=4\sqrt{5}$

Finally, the correct option is:

<em>Four square root of five</em>

4 0

3 years ago

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Question 4 Given: f(x) = -3x – 3 and g(x) = x2 + 5 Find (f - g) ().

Aleonysh [2.5K]

Answer:

We get $\mathbf{(f-g)(x)= -x^2-3x-8}$

Step-by-step explanation:

We are given:

$f(x) = -3x - 3\\ g(x) = x^2 + 5$

We need to find (f-g)(x) (assuming there is x in the bracket, i.e. (f - g) () should be (f-g)(x))

We would simply subtract f(x) and g(x)

$(f-g)(x)\\= -3x-3-(x^2+5)\\Multiply\:minus\:sign\:with\:terms\:inside\:the\:bracket\\=-3x-3-x^2-5\\Combining\:like\:terms:\\=-x^2-3x-3-5\\=-x^2-3x-8$

So, We get $\mathbf{(f-g)(x)= -x^2-3x-8}$

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3 years ago

What number multiples to -12 and adds to 4 (factoring: diamond method)

Marizza181 [45]

Answer: - 2 and 6

Step-by-step explanation:

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3 years ago

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Write in point slope form of the line that passes through the points (3,-1) and (6,-2)

skelet666 [1.2K]

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-(-1)}{6-3}\implies \cfrac{-2+1}{3}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=-\cfrac{1}{3}(x-3)\implies y+1=-\cfrac{1}{3}(x-3)$

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3 years ago