1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lesya [120]
2 years ago
13

A real estate agent has 8 master keys to open several new homes. Only 1 master key will open any given house. If 40% of these ho

mes are usually left unlocked, what is the probability that the real estate agent can get into a specific home if the agent selects 3 master keys at random before leaving the office?
Mathematics
1 answer:
riadik2000 [5.3K]2 years ago
5 0

Answer:

Step-by-step explanation:

Suppose F represents the value that a room is unlocked.

Then, we can assume that the probability of unlocked homes is:

P(unlocked homes) = P(U)

P(unlocked homes) = 40%

P(unlocked homes) = 0.40

Also, let us represent the value of the locked room with G.

P(locked homes) = P(G)

P(locked homes) = (1 - 0.40)

P(locked homes) = 0.60

Let the probability of selecting a correct key be P(S)

It implies that for the agent to use 3 keys, we have a combination of ^8C_3 possible ways for the set of keys.

Now; since only one will open the house, then:

P(select correct key) = P(S)

P(S) = \dfrac{ (^1_1) (^7_2)   }{   ^8_3 }

P(S) = \dfrac{21}{56}

P(S) = 0.375

Finally, for the real estate agent to have access to specific homes supposing the agent select three master keys at random prior to the time he left his office, Then:

P(F ∪ (G∩S) = P(F) + P(G∩S)

P(F ∪ (G∩S) = P(F) + P(G) × P(S)

P(F ∪ (G∩S) = 0.40 + (0.60×0.375)

P(F ∪ (G∩S) = 0.40 + 0.225

P(F ∪ (G∩S) =0.625

You might be interested in
The coefficient of kinetic friction between an object and the surface upon which it is sliding is 0.43. The mass of the object i
brilliants [131]

Answer:

14 x 0.27 = 3.78 is your answer

Explanation:

the question is asking for the weight of the object so you multiply and get 3.79

7 0
2 years ago
If f(x) = │(x² – 50)│, what is the value of f(-5) ?
Liula [17]
f(x)=|(x^2-50)|\\\\f(-5)=|(-5)^2-50|=|25-50|=|-25|=25\\\\\\|a|=  \left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a < 0\end{array}\right\\\\|-3|=3;\ |5|=5;\ |0|=0;\ |-12|=12
5 0
3 years ago
Read 2 more answers
2x+1y=25 <br> find the equation of x
leonid [27]

Answer:

x=

−1

2

y+

25/2

Step-by-step explanation:

Let's solve for x.

2x+1y=25

Step 1: Add -y to both sides.

2x+y+−y=25+−y

2x=−y+25

Step 2: Divide both sides by 2.

2x

2

=

−y+25

2

x=

−1

2

y+

25

2

8 0
2 years ago
The factory receives an order for more than 1,100 boxes. Machine B has already packed 55 boxes. Write and solve an inequality to
Softa [21]

Answer:

<h2>no lo sé <u>pero</u><u> </u><u>te</u><u> </u><u>ayudaría</u><u> </u><u>si</u><u> </u><u>lo</u><u> </u><u>supiera</u><u> </u></h2>
7 0
2 years ago
Find thetwo consecutive integers whose product is 24​
malfutka [58]

Answer:

There is no solution to this equation that is an integer for x.

Step-by-step explanation:

x is the first integer, and x+1 the second

x(x+1) = 24\\x^{2} + x - 24 =0\\

x = \frac{-1+\sqrt{1^{2}+4*24}}{2} =\frac{-1+\sqrt{97}}{2}\\x = \frac{-1-\sqrt{1^{2}+4*24}}{2} =\frac{-1-\sqrt{97}}{2}

5 0
2 years ago
Other questions:
  • Find the area of the shaded region. Round to the nearest tenth if necessary.
    12·1 answer
  • Easy Geometry Riddle
    13·2 answers
  • Robert is lying on the ground, looking at the top of a flagpole. The angle of elevation to the top of the flagpole is 25°. What
    11·1 answer
  • Which of the following number odd<br>​
    7·2 answers
  • Help ineed help its just too much too count im so confused #screwfortnite
    8·2 answers
  • Click on the solution set below until the correct one is displayed
    11·1 answer
  • What is 12.95p=44 simplified to its lowest value
    14·1 answer
  • #26: Identify the domain. <br><br> {(1,-3), (3,1),(5,5), (7,9), (9,13)}
    7·1 answer
  • MAX POINTS
    6·1 answer
  • Which expression is equivalent to<br><br> (x^6y^8)^3/ x^2y^2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!