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two numbered 1 to 6 dice are thrown together and their scores are added. the probability that the sum will be 4 is?

natulia [17]

Answer:

$Pr = \frac{3}{36}$

Step-by-step explanation:

Given

2 number die

Required

P(Sum = 4)

The sample space of 2 die is:

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

$(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6), (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)$

$(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6), (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)$

$n(S)= 36$

The pairs that adds up to 4 are:

$Sum(4) = \{(1,3), (2,2),(3,1)\}$

$n(Sum) =3$

So, the probability is:

$Pr = \frac{n(Sum)}{n(S)}$

$Pr = \frac{3}{36}$

5 0

3 years ago

Recall from Intermediate Algebra that two non-vertical lines are perpendicular if and only if they have negative reciprocal slop

OLEGan [10]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The line is $y = -4 x$

Step-by-step explanation:

From the question we are told that

The line is $y = \frac{1}{4} x + 8$

The point is P(0,0 )

Generally the equation for a line is $yn = mx + c$

Now comparing this with the given equation we see that

$m =\frac{1}{4} = slope$

$C =8 = intercept$

Generally the slope of the perpendicular to the given line is mathematically evaluated as

$m_1 = - \frac{1}{m}$

=> $m_1 = - \frac{1}{ \frac{1}{4}}$

=> $m_1 = -4$

Generally from the univesal equation of a line and the given point we have that

y = mx + c at p(0,0) and $m_1 = -4$ is

0 = -4 (0 ) + c

=> c = 0

Hence the equation perpendicular to the line given at the point given is

$y = -4 x$

8 0

3 years ago

Whats the area?Answer this ASAP plz

DochEvi [55]

Answer:

that is the solution to the question

7 0

4 years ago

Read 2 more answers

Find the slope of each line 2-3. please help thank you.

atroni [7]

2)
(-3, 3) (2,0)
slope = (3-0)/(-3-2) = -3/5

3)
y = 3
so slope = 0

7 0

3 years ago

A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

Cloud [144]

Answer:

$z=\frac{13-20}{4}=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu$

$p_v = P(Z$

Step-by-step explanation:

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".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

$X \sim Binom(n=100, p=0.2)$

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:

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

We need to check the conditions in order to use the normal approximation.

$np=100*0.2=20 \geq 10$

$n(1-p)=20*(1-0.2)=16 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=100*0.2=20$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$