Ask question

Ask question

All categories

2 days ago

13

The Florida Tourist Commission selected a random sample of 200 people that attended one or more concerts during the first weeken

d in April of 2010. The survey revealed that 120 concert goers went to Orlampa Skydome and 100 went to the Bithlo Megaplax. Calculate the probability that a selected concert goer during the same weekend next year will go to either the Orlampa Skydome OR the Bithlo Megaplax?

1 answer:

Inessa [12.1K]2 days ago

6 0

Answer:

0.8 or 80%

Step-by-step explanation:

Let A and B denote the different events

A: “The concert attendee visited Orlampa Skydome”

B: “The concert attendee visited the Bithlo Megaplax”

Thus, the probability P(A) of a concert attendee visiting Orlampa Skydome is

P(A) = 120/200 = 0.6

In a similar manner,

P(B) = 100/200 = 0.5

We seek to determine P(A∪B), which represents the odds that a concert attendee went to either Orlampa Skydome OR the Bithlo Megaplax.

We know that

P(A∪B) = P(A) + P(B) - P(A∩B)

but P(A∩B) signifies the possibility that a concert attendee went to both Orlampa Skydome AND the Bithlo Megaplax.

Given that the events are independent,

P(A∩B) = P(A)P(B) = 0.6*0.5 = 0.3

and

P(A∪B) = 0.6 +0.5 - 0.3 = 0.8 or 80%

You might be interested in

An old-fashioned Chinese restaurant offers a family dinner where you get to choose one dish from “column A” (which has 8 dishes)

Zina [11989]

The result is calculated as 10 multiplied by 8 multiplied by 5, which equals 400.

7 0

9 days ago

Read 2 more answers

A CD has a 5% chance of being a smash hit and profiting $5.2 million, a 50% chance of being a modest success and profiting $0.9

Zina [11989]

P(S) = Probability of Smash = 0.05 (5%)
P(M) = Probability of Modest = 0.5 (50%)
P(F) = Probability of Flop = 0.45 (45%)
Based on this, we utilize the model for discrete random variables, leading to:
E(X) = (0.05 * 5.2) + (0.5 * 0.9) + (0.45 * 0)
= 0.26 + 0.45 + 0
= 0.71 Mill'

5 0

1 month ago

sari has 3 times as many pencil erasers Sam. Together, they have 28 erasers. How many erasers does Sari have

PIT_PIT [11918]

Start by letting x represent the number of Sam's pencils. Then Sari has 3x (since she has three times as many)

Together they total 28 pencils:
x + 3x = 28
4x = 28 /:4 (divide both sides by 4)
x = 7
So Sam has 7 pencils.
Sari, having three times as many, has 7 * 3 = 21.[[TAG_8]]

4 0

22 days ago

Read 2 more answers

Let P be a point not on the line L that passes through the points Q and R. The distance d from the point P to the line L is d =

AnnZ [11902]

Answer:

The distance from the point (0,1,1) to the specified line is zero.

Step-by-step explanation:

Considering the parametric equations of the line,

x=2t, y=5-2t, z=1+t

In order to calculate the distance from (0,1,1), we must remove t from the equations above, such that

$y=5-2t=5-x\implies x+y=5=4+1=4+z-t=4+z-\frac{1}{2}x$

$\implies 3x+2y-2z-8=0\hfill (1)$

whose direction ratios are (l,m,n)=(3,2,-2) and the distance from point (a,b,c)=(0,1,1) is defined as

$\frac{al+bm+cn}{\sqrt{l62+m^2+n^2}}=\frac{(3\times 0)+(2\times 1)+(-2)(1)}{\sqrt{3^2+2^2+(-2)^2}}=\frac{0+2-2}{\sqrt{17}}=0$

The distance between the point (0,1,1) and (1) amounts to zero. Therefore, the point (0,1,1) is located on the line (1).

8 0

26 days ago

Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Inessa [12141]

Answer:

Wyjaśnienie krok po kroku:

Załóżmy, że prostokąt ma wierzchołki (x,y,z) w dodatnim oktancie. Prostokątny pudełko musi być symetryczne względem wszystkich trzech osi.

Wtedy jego boki to

$2x,2y,2z$

Objętość = $8xyz$

Maksymalizuj objętość przy założeniu

$x^2+y^2+z^2 =1$

tj. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Użyj mnożników Lagrange'a, mamy

$∇f(x,y,z)=λ∇g(x,y,z)$ przy maksimum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

$8yz=2λx8xz=2λy8xy=2λz$

Dzieląc otrzymujemy

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Podobnie $y^2=z^2$

Zatem otrzymujemy $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Stąd wymiary to

(2x,2y,2z)

<pzatem wymiary="" to="">

$\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} } )$

</pzatem>

3 0

1 month ago