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
Lostsunrise [7]
3 years ago
10

An individual repeatedly attempts to pass a driving test. Suppose that the probability of passing the test with each attempt is

0.25, and that the results of successive tests are independent. Let X be the number of tests taken until the individual passes (a) Find the probability mass function of X (b) Evaluate the probability of passing the test with three or less attempts. (c) Evaluate the probability of passing the test with five or more attempts.
Mathematics
1 answer:
vladimir1956 [14]3 years ago
3 0

Answer:

a) Our random variable X="number of tests taken until the individual passes" follows a geomteric distribution with probability of success p=0.25

For this case the probability mass function would be given by:

P(X= k) = (1-p)^{k-1} p , k = 1,2,3,...

b) P(X \leq 3) = P(X=1) +P(X=2) +P(X=3)

P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25

P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875

P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406

And adding the values we got:

P(X \leq 3) =0.25+0.1875+0.1406=0.578

c) P(X \geq 5) = 1-P(X

And we can find the individual probabilities:

P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25

P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875

P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406

P(X= 4) = (1-0.25)^{4-1} *0.25 = 0.1055

P(X \geq 5) = 1-[0.25+0.1875+0.1406+0.1055]= 0.316

Step-by-step explanation:

Previous concepts

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

P(X=x)=(1-p)^{x-1} p

Let X the random variable that measures the number of trials until the first success, we know that X follows this distribution:

X\sim Geo (1-p)

Part a

Our random variable X="number of tests taken until the individual passes" follows a geomteric distribution with probability of success p=0.25

For this case the probability mass function would be given by:

P(X= k) = (1-p)^{k-1} p , k = 1,2,3,...

Part b

We want this probability:

P(X \leq 3) = P(X=1) +P(X=2) +P(X=3)

We find the individual probabilities like this:

P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25

P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875

P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406

And adding the values we got:

P(X \leq 3) =0.25+0.1875+0.1406=0.578

Part c

For this case we want this probability:

P(X \geq 5)

And we can use the complement rule like this:

P(X \geq 5) = 1-P(X

And we can find the individual probabilities:

P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25

P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875

P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406

P(X= 4) = (1-0.25)^{4-1} *0.25 = 0.1055

P(X \geq 5) = 1-[0.25+0.1875+0.1406+0.1055]= 0.316

You might be interested in
The combined weight of the people in an elevator is 49% of the 3,025-pound capacity.Which would be the best way to estimate the
klasskru [66]

Answer:

50% of 3000

Step-by-step explanation:

49% is very close to 50% (half).  3,025 pounds is very close to 3,000 pounds.

Half of 3,000 pounds is 1,500 pounds.

3 0
2 years ago
Given the values in the table on the left come from
schepotkina [342]

–3.2 < x < –2.4

1.6 < x < 2.4

7 0
3 years ago
What are the solutions to the system of equations? y=2x^2−6x+3 y=2x+3
adoni [48]

Answer:

Step-by-step explanation:

y=2x²-6x+3

y=2x+3

2x²-6x+3=2x+3

2x²-6x+3-2x-3=0

2x²-8x=0

2x(x-4)=0

x=0,4

y=0+3=3

and y=2(4)+3=11

so solutions are (0,3) and (4,11)

5 0
2 years ago
Answer asap pls no wrong answers pls
Vlad1618 [11]

Answer:

(-1.1)

Step-by-step explanation:

i dont if is right just tring yo help

6 0
3 years ago
(+8) + (-9) <br> Equal what ??
Tanzania [10]
(+8)+(-9) 
the answer is -1
5 0
3 years ago
Read 2 more answers
Other questions:
  • The following lists show the free throw percentages of 16 players for the Detroit Pistons and Miami Heat during the 2012-2013 NB
    15·1 answer
  • What best describes a triangle with angles measuring 60 degrees 40 degrees and 100 degrees
    14·1 answer
  • Am I correct on #13? ONLY REAL ANSWRS OR YOULL GET REPORTED
    14·1 answer
  • Determine the type and degree of each of the following polynomial expressions
    9·1 answer
  • There are 24 sixth graders and 32 seventh graders attending an after school event. For this event, sixth graders and 7th graders
    7·1 answer
  • How do i solve this?
    14·1 answer
  • Y divided by 3 is equal to 15
    9·2 answers
  • Round 1,658.013 to the nearest hundred
    11·2 answers
  • State whether the following statements are true or false mathematics.<br><img src="https://tex.z-dn.net/?f=%20%5Cgeqslant" id="T
    14·2 answers
  • Use intercepts to graph the line described by the equation.<br><br> 2y = −10x − 20
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!