What is the total cost if you buy 3 goldfish for $1.90 each, 3 angelfish for $6.10 each, and 12 neon tetras for $1.53 each?

A survey is conducted to find out whether people in metropolitan areas obtain their news from television (Event T), an newspaper

MrMuchimi

Answer:

e) P ( R' | T ) = 0.62857

f) P ( T' | N ) = 0.32258

g) P ( R' | N ) = 0.70968

h) P ( T' | N&R ) = 5/6

Step-by-step explanation:

Given:

- The probability of Television as news source P ( T ) = 0.7

- The probability of Newspaper as news source P ( N ) = 0.62

- The probability of Radio as news source P ( R ) = 0.46

- The probability of Television & Newspaper as news source P (T&N) = 0.42

- The probability of Television & Radio as news source P (T&R) = 0.26

- The probability of Radio & Newspaper as news source P (R&N) = 0.18

- The probability of all 3 as news source P ( T & R & N ) = 0.03

Find:

Given that TV is a news source, what is the probability that radio is not a news source?

Given that newspaper is a news source, what is the probability that TV is not a news source?

Given that newspaper is a news source, what is the probability that radio is not a news source?

Given that both newspaper and radio are news sources, what is the probability that TV is not a news source?

Solution:

- We will first compute the individual probability of each event occurring alone.

P (Television is the only news source) = P(T) - P(T&R) - P(T&N) + P(T&N&R)

P ( Only Television ) = P ( only T ) = 0.7 - 0.42 - 0.26 + 0.03 = 0.05

P (Newspaper is the only news source) = P(N)-P(N&R)-P(T&N)+P(T&N&R)

P ( Only Newspaper ) = P ( only N ) = 0.62 - 0.18 - 0.42 + 0.03 = 0.05

P (Radio is the only news source) = P(R) - P(T&R) - P(N&R) + P(T&N&R)

P ( Only Radio ) = P ( only R ) = 0.46 - 0.26 - 0.18 + 0.03 = 0.05

- Now for part e)

We are asked for a conditional probability of the form as follows:

P ( R' | T ) = P ( R' & T ) / P ( T )

First compute the probability that next news source is not Radio provided it is already a source of TV.

P ( R' & T ) = P( only T ) + P ( only T & N ) = 0.05 + 0.42 - 0.03 = 0.44

Hence,

P ( R' | T ) = 0.44 / 0.7

P ( R' | T ) = 0.62857

- Now for part f)

We are asked for a conditional probability of the form as follows:

P ( T' | N ) = P ( T' & N ) / P ( N )

First compute the probability that next news source is not TV provided it is already a source of Newspaper.

P ( T' & N ) = P( only N ) + P ( only R & N ) = 0.05 + 0.18 - 0.03 = 0.2

Hence,

P ( T' | N ) = 0.2 / 0.62

P ( T' | N ) = 0.32258

- Now for part g)

We are asked for a conditional probability of the form as follows:

P ( R' | N ) = P ( R' & N ) / P ( N )

First compute the probability that next news source is not Radio provided it is already a source of Newspaper.

P ( R' & N ) = P( only N ) + P ( only T & N ) = 0.05 + 0.42 - 0.03 = 0.44

Hence,

P ( R' | N ) = 0.44 / 0.62

P ( R' | N ) = 0.70968

- Now for part h)

We are asked for a conditional probability of the form as follows:

P ( T' | N&R ) = P ( T' & N & R) / P ( N & R )

First compute the probability that next news source is not TV provided it is already a source of both radio and Newspaper.

P ( T' & N & R) = P ( only N & R ) = 0.18 - 0.03 = 0.15

Hence,

P ( T' | N&R ) = 0.15 / 0.18

P ( T' | N&R ) = 5/6

6 0

3 years ago

If f(1) = 160 and f(n + 1) = –2f(n), what is f(4)?

balandron [24]

Answer with Step-by-step explanation:

f(1) = 160 and f(n + 1) = –2f(n)

⇒ f(2)= -2×f(1)

= -2×160

= -320

⇒ f(3)= -2×f(2)

= -2×(-320)

= 640

⇒ f(4)= -2×f(3)

= -2×640

= -1280

Hence, Value of f(4) is:

- 1280

7 0

3 years ago

The height and radius of a right cylinder are each 6 cm.

Marianna [84]

The volume of a cylinder can be found using the formula πr²h.

V = (3.14)(6)²(6)
V = 678.24 cm³

From the answer choices it will be:

V = π(6)²(6)
V = 216π cm³

So the answer is answer choice B.

Hope this helps :)

8 0

4 years ago

Read 2 more answers

a restaurant has an all-you-can-eat buffet. They charge $13.95 per person. what is the constant of proportionality?

Evgen [1.6K]

Answer:

staurant has an all-you-can-eat buffet. They charge $13.95 per person. what is the constant of proportionality?

Step-by-step explanation:

3 0

4 years ago

Which answer does NOT correctly describe the graph of y = 5x + 12?

Svetlanka [38]

<h2>Answer</h2>

2. The Graph Contains The Point (5, 12)

<h2>Explanation</h2>

Remember that in a linear function of the form $y=mx+b$ , $m$ is the slope/rate of change of the line and $b$ is the y-intercept.

From our equation we can infer that $b=12$ , so the y-intercept of our graph is 12 units above the origin on the point (0, 12). Therefore, choice 2 correctly describe the graph of y = 5x + 12

We can also infer that $m=5$ , so the slope of our line is 5, which is constant, so our line has a constant rate of change. Also, since every integer can be written as a fraction with denominator 1, we can write our slope as $m=\frac{5}{1}$ . Therefore, choices 1 and 2 correctly describe the graph of y = 5x + 12.

Now, remember that any point on the plane has coordinates $(x,y)$ , so, to check if a point is on a line, we just need to replace the $x$ and $y$ values in the line equation and check if the equation holds. Our point is (5, 12), so x = 5 and y = 12. Lets replace the values in our line:

$y=5x+12$

$12=5(5)+12$

$12=25+12$

$12\neq 37$

Since the equation equation doesn't hold (12 is not equal 37), we can conclude that the graph doesn't contain the point (5, 12). Therefore, choice 2 does NOT correctly describe the graph y = 5x +12.

7 0

4 years ago

Read 2 more answers