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
ludmilkaskok [199]
3 years ago
10

A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at ea

ch answer. Let X be the number of questions the student gets correct. (a) Find P(X = 3). (b) Find P(X > 2). (c) To pass the test, the student must answer 7 or more questions correctly. Would it be unusual for the student to pass? Explain.
Mathematics
1 answer:
slamgirl [31]3 years ago
7 0

Answer:

1)0.2502

2)0.475

3)0.003505

Step-by-step explanation:

Total No. of question n= 10

There are four choices in each question

So, Probability of success p = \frac{1}{4}

Probability of failure q  = 1- \frac{1}{4}=\frac{3}{4}

We will use binomial over here

P(X=x)=^nC_r p^r q^{n-r}

1)

P(X = 3)=^{10}C_3 (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=\frac{10!}{3!7!} (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=0.2502

2)  P(X > 2)=1-P(X\leq 2)

P(X>2)=1-(P(X=0)+P(X=1)+P(X=2))

P(X>2)=1-(^{10}C_0 (\frac{1}{4})^0 (\frac{3}{4})^{10}+(^{10}C_1 (\frac{1}{4})^1 (\frac{3}{4})^9+^{10}C_2 (\frac{1}{4})^2 (\frac{3}{4})^8)

P(X>2)=1-((\frac{1}{4})^0 (\frac{3}{4})^{10}+(\frac{10!}{1!9!} (\frac{1}{4})^1 (\frac{3}{4})^9+\frac{10!}{2!8!}  (\frac{1}{4})^2 (\frac{3}{4})^8)

P(X>2)=0.475

3)

P(X\geq 7)=P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\P(X\geq 7)=^{10}C_7 (\frac{1}{4})^7 (\frac{3}{4})^{3}+(^{10}C_8 (\frac{1}{4})^8 (\frac{3}{4})^2+^{10}C_9 (\frac{1}{4})^9 (\frac{3}{4})^1+^{10}C_{10} (\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=\frac{10!}{7!3!} (\frac{1}{4})^7 (\frac{3}{4})^{3}+\frac{10!}{8!2!} (\frac{1}{4})^8 (\frac{3}{4})^2+\frac{10!}{9!1!} (\frac{1}{4})^9 (\frac{3}{4})^1+\frac{10!}{10!0!}(\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=0.003505

You might be interested in
What is 1 tenth of 2.0
timofeeve [1]
O.2 0.2 0.2 the answer is 0.2
yeah
6 0
3 years ago
Read 2 more answers
Please help me! What is the simplest form for 21 /63 ?
creativ13 [48]

Answer:

1/3

Step-by-step explanation:


5 0
3 years ago
Can we get the steps please?
evablogger [386]
Using the Slope Equation
Pick two points on the line and determine their coordinates.
Determine the difference in y-coordinates of these two points (rise).
Determine the difference in x-coordinates for these two points (run).
Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
3 0
3 years ago
You are hosting a convention for a charitable organization. You pay a rental fee of $28,500 for the convention center, plus you
Alexxandr [17]
You have to add the $51 to $13 and find the answer then divide the sum by $28,500
8 0
3 years ago
Read 2 more answers
Sam drove 320 miles in 2.5 hours, how long will it take to drive 500 at the same rate (speed)?
marishachu [46]

Answer:

D = (55)(4.5)  

425 = 60 T  

200 = R (2.5)  

4.6 hours  

59 mph  

217 miles




Step-by-step explanation:


6 0
3 years ago
Other questions:
  • What kind of transformation converts the graph of f(x) = 10x + 71 - 2 into the graph of
    15·1 answer
  • 1. A sample is being chosen for a survey to find out how people feel about adding more stop signs near a school. Which group wou
    5·1 answer
  • Solve by substitution the following problem please y=10.20x+2500
    15·1 answer
  • 5(y + 2/5) = -13<br><br> Solve for y<br><br> Show or explain your method
    5·2 answers
  • Please help me !!!!!
    5·1 answer
  • Please help this is not correct !
    14·1 answer
  • Find the solution set for 8x - 3 = 2(x - 1/2)​
    13·1 answer
  • Sunita performed a transformation on trapezoid LMNQ to create L′M′N′Q′, as shown in the figure below:
    8·1 answer
  • Please help me....
    15·1 answer
  • A class has 28 students 13 boys and 15 girls what is rstio girls to boys
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!