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2 years ago

If you roll two fair six-sided dice what is the probability that the sum is:

Mathematics

1 answer:

blsea [12.9K]2 years ago

6 0

Answer: If you roll two fair six-sided dice, the probability that the sum is 5 or lower is 5/18.

Explanation: Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

For an experiment having n number of outcomes, the number of favorable outcomes can be denoted by x

Let ‘x’ be the number on the first dice.

‘Y’ be the number on second dice.

We have to find the probability that the sum is 5 or lower i.e. (x + y) <= 5.

Total number of possible results from two six-sided dice is 6 × 6 = 36.

The possible results that the sum is lower than 4 is (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2) and (4,1).

Number of possible results for the sum is 5 or lower is 10.

The probability that the sum is 5 or lower = 10/36

=5/18

Therefore, the probability that the sum is 5 or lower is 5/18.

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Help me please 9 - 4(2p - 1) = 41

dem82 [27]

Answer:

p = -3.5

Step-by-step explanation:

Simplifying

9 + -4(2p + -1) = 41

Reorder the terms:

9 + -4(-1 + 2p) = 41

9 + (-1 * -4 + 2p * -4) = 41

9 + (4 + -8p) = 41

Combine like terms: 9 + 4 = 13

13 + -8p = 41

Solving

13 + -8p = 41

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-13' to each side of the equation.

13 + -13 + -8p = 41 + -13

Combine like terms: 13 + -13 = 0

0 + -8p = 41 + -13

-8p = 41 + -13

Combine like terms: 41 + -13 = 28

-8p = 28

Divide each side by '-8'.

p = -3.5

Simplifying

p = -3.5

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1 year ago

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Please help, showing work is not necessary but appreciated.<br> Find the sum.

marishachu [46]

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4 years ago

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A study of consumer smoking habits includes A people in the 18-22 age bracket (B of whom smoke), C people in the 23-30 age brack

madreJ [45]

The correct question is:

A study of consumer smoking habits includes 167 people in the 18-22 age bracket (59 of whom smoke), 148 people in the 23-30 age bracket (31 of whom smoke), and 85 people in the 31-40 age bracket (23 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes

Answer:

The probability of getting someone who is age 23-30 or smokes = 0.575

Step-by-step explanation:

We are given;

Number consumers of age 18 - 22 = 167

Number of consumers of ages 22 - 30 = 148

Number of consumers of ages 31 - 40 = 85

Thus,total number of consumers in the survey = 167 + 148 + 85 = 400

We are also given;

Number consumers of age 18 - 22 who smoke = 59

Number of consumers of ages 22 - 30 who smoke = 31

Number of consumers of ages 31 - 40 who smoke = 23

Total number of people who smoke = 59 + 31 + 23 = 113

Let event A = someone of age 23-30 and event B = someone who smokes. Thus;

P(A) = 148/400

P(B) = 113/400

P(A & B) = 31/400

Now, from addition rule in sets which is given by;

P(A or B) = P (A) + P (B) – P (A and B)

We can now solve the question.

Thus;

P(A or B) = (148/400) + (113/400) - (31/400)

P(A or B) = 230/400 = 0.575

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3 years ago

Stats To quality for a police academy, applicants are given a lest of physical Itness. Ihe scores are normallyDistributed with a

omeli [17]

Since we want just the top 20% applicants and the data is normally distributed, we can use a z-score table to check the z-score that gives this percentage.

The z-score table usually shows the percentage for the values below a certain z-score, but since the whole distribution accounts to 100%, we can do the following.

We want a z* such that:

$P(z>z^*)=0.20$

But, to use a value that is in a z-score table, we do the following:

$\begin{gathered} P(zz^*)=1 \\ P(zz^*)=1-0.20=0.80 \end{gathered}$

So, we want a z-score that give a percentage of 80% for the value below it.

Using the z-score table or a z-score calculator, we can see that:

$\begin{gathered} P(zNow that we have the z-score cutoff, we can convert it to the score cutoff by using:[tex]z=\frac{x-\mu}{\sigma}\Longrightarrow x=z\sigma+\mu$

Where z is the z-score we have, μ is the mean and σ is the standard deviation, so:

$\begin{gathered} x=0.8416\cdot9+64 \\ x=7.5744.64 \\ x=71.5744\cong72 \end{gathered}$

so, the cutoff score is approximately 72.

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1 year ago

Write an equation in standard form of the line passing through the points (12, 3) and (-3, 8).

aliya0001 [1]

Answer:

x + 3y = 21

Step-by-step explanation:

$(x_{1},y_{1})=(12,3) \\\\(x_{2},y_{2})=(-3,8)\\\\Slope= \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\= \dfrac{8-3}{-3-12}= \dfrac{5}{-15}\\\\= \dfrac{-1}{3}$

Equation of the line: y =mx+ b

$y = \dfrac{-1}{3}x+b\\\\\\Plugin \ x = 12 \ and \ y=3 \ in \ the \ above \ equation\\\\3= \dfrac{-1}{3}*12+b\\\\3= -4+b\\\\3+4 = b\\\\b = 7\\\\\\\y= \dfrac{-1}{3}x+7\\\\$

Multiply the equation by 3

3y = -x + 21

x + 3y = 21

6 0

3 years ago