MATHEMATICS COLLEGE

Out of 100 emails, 60 are spam and 48 of those contain the word buy. Of the remaining 40 emails that are not spam, only 4 emails contain the word buy. Given that an email is spam, what is the probability that it contains the word buy?

Answers

Answer 1

Answer: 48/60 or 0.8 if you know it's spam already, but 0.48 if you are picking randomly from 100 emails

Answer 2

Answer:

Answer:

its .8 for plato students

Step-by-step explanation:

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Suppose a quiz contains 20 true/false questions. You know the correct answer to the first 10 questions. You have no idea of the correct answer to questions 11 through 20 and decide to answer each using the coin toss method. Calculate the probability of obtaining a total quiz score of at least 85%

Answers

Answer:

0.1719

Step-by-step explanation:

Given that:

A quiz contains 20 questions and 10 questions have been answered rightly

We are to determine the probability of getting a total quiz score of 85%

i.e 0.85 (20) = 17

Let's not forget that 10 is correctly answered out of 17. that implies that we only have 7 more questions to make a decision on.

where;

n = 10,

p + q = 1, 0.5 + q = 1

q = 1 - 0.5

q = 0.5

Let X be the random variable that follows the binomial distribution. Then ;

$P(X = x) =(^n_x) p^x q^(n -x)$

where x = 7

$P(X \geq 7) =P(X=7)+P(X=8)+P(X=9)+P(X=10)$

$P(X \geq 7) =(^(10)_7})\ 0.5^7 \ 0.5 ^(10-7) + (^(10)_(8))\ 0.5^8 \ 0.5 ^(10-8)+(^(10)_9})\ 0.5^9 \ 0.5 ^(10-9)+ (^(10)_(10)})\ 0.5^(10) \ 0.5 ^(10-10)$

P(X ≥ 7) = 0.1719

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate.

Answers

The question is incomplete. Here is the complete question.

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, 63% of planted seeds will germinate. A random sample of 9 seeds is chosen. If these seeds are planted according to the instructions, find the probability that 4 or 5 of them germinate. Do not round your intermiediate computations, and round your answer to three decimal places.

Answer: P(4<X<5) = 0.624

Step-by-step explanation: The probability of a seed germinate is a BinomialDistribution, i.e., a discrete probability distribution of the number of successes in a sequence of n independents experiments.

This distribution can be approximated to normal distribution by determining the values of mean and standard deviation population:

$\mu=np$

$\sigma=√(np(1-p))$

where

n is the sample quantity

p is proportion of successes

For the spinach seeds:

Mean is

$\mu=9(0.65)$

$\mu=$ 5.85

Standard deviation is

$\sigma=√(9.0.65(1-0.65))$

$\sigma=$ 1.431

Now, use

$z=(x-\mu)/(\sigma)$

to convert into a standard normal distribution.

The probability we want is between 2 values: P(4<X<5).

Therefore, we have to convert those two values:

For X = 4:

$z=(4-5.85)/(1.431)$

z = -1.29

For X = 5:

$z=(5-5.85)/(1.431)$

z = -0.59

Using z-table:

P(X>4) = 1 - P(z< -1.29) = 0.9015

P(X<5) = P(z< -0.59) = 0.2776

The probability will be

P(4<X<5) = P(X>4) - P(X<5)

P(4<X<5) = 0.9015 - 0.2776

P(4<X<5) = 0.624

The probability of 4 or 5 seeds germinate is0.624.

Decide on what substitution to use, and then evaluate the given integral using a substitution.(Remember to use absolute values where appropriate.) ∫ [(x⁵− x⁴) / (5x6 − 6x5)] dx

Answers

Answer:

The answer is $(1)/(30)\Big[2\log x-\log 6\Big]$

Step-by-step explanation:

Given,

$\int (x^(5)-x^(4))/(5x^(6)-6x^5)dx$

$=\int (x^4(x-1))/(x^5(5x-6))dx$

$=(1)/(6)\int\Big[(1)/(x)+(1)/(5x-6)\Big]dx$

$=\fracd{1}{6}\int (1)/(x)dx+(1)/(6* 5)\int(5)/(5x-6)dx$

$=(1)/(30)\Big[5\log x +\log (5x-6)\Big]$

$=(1)/(30)(2\log x-\log 6)$

Hence the result.

Quadrilateral MBPV is similar to quadrilateral GKDF. BP = 78 mm, KD = 30 mm , and FD = 45 mm. What is VP? Enter your answer in the box □mm.

Answers

Answer:

VP = 117 mm

Step-by-step explanation:

Corresponding sides of similar quadrilaterals are proportional.

VP/FD = BP/KD

VP = FD·BP/KD = (45 mm)·(78/30) . . . . multiply by FD; fill in the givens

VP = 117 mm

You and a group of friends are going to a five-day outdoor music festival during spring break. You hope it does not rain during the festival, but the weather forecast says there is a 15% chance of rain on the first day, a 10% chance of rain on the second day, a 20% chance of rain on the third day, a 20% chance of rain on the fourth day, and a 60% chance of rain on the fifth day. Assume these probabilities are independent of whether it rained on the previous day or not. What is the probability that it does not rain during the entire festival

Answers

Answer:

Probability that it does not rain during the entire festival = 0.19584

Step-by-step explanation:

We are given that you and a group of friends are going to a five-day outdoor music festival during spring break.

Also, Probability that there may be rain on first day, P(A) = 0.15

Probability that there may be rain on second day, P(B) = 0.10

Probability that there may be rain on third day, P(C) = 0.20

Probability that there may be rain on fourth day, P(D) = 0.20

Probability that there may be rain on fifth day, P(E) = 0.60

It is also provided that these probabilities are independent of whether it rained on the previous day or not.

Now, probability that it does not rain during the entire festival = Probability that there may not be rain on all five days

= (1 - P(A)) $*$ (1 - P(B)) $*$ (1 - P(C)) $*$ (1 - P(D)) $*$ (1 - P(E))

= (1 - 0.15) $*$ (1 - 0.10) $*$ (1 - 0.20) $*$ (1 - 0.20) $*$ (1 - 0.60)

= 0.85 $*$ 0.90 $*$ 0.80 $*$ 0.80 $*$ 0.40 = 0.19584

(1 point) The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 20 Southwest flights and observing whether they arrive on time.

Answers

Answer:

No. Southwest flights did not arrive on time.

Step-by-step explanation:

Please see attachment

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The following EXCEL tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course. Regression Statistics Multiple R 0.142620229 R Square 0.02034053 Standard Error 20.25979924 Observations 22 Coefficients Standard Error T Stat P-value Intercept 39.39027309 37.24347659 1.057642216 0.302826622 Attendance 0.340583573 0.52852452 0.644404489 0.526635689 What is the predicted value received on an exam when Percentage Attendance = 70 a. Approximately 63 b. Approximately 2758 c. Approximately 40 d. Approximately 70