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
A bus covers a certain distanc in 45 minutes if it runs at a Speed of 60km/hr. What must be the speed of the bus in order to red
Ket [755]

2.66 is the speed

..................................................................................................................................................................................................................................................................................................................................................................................................................................

8 0
1 year ago
A randomly generated list of numbers from 0 to 4 is being used to simulate an event with numbers 3 and 4 representing a success.
Whitepunk [10]
The answer is D, 40%. I got it by knowing that 3 and 4 were the success numbers and that 0,1, and 2 were unsuccessful and that numbers 3 and 4 are less than half, so I went with 40% and it was right. Good luck apex! Finish strong!
5 0
3 years ago
Stephen record the growth of a plant over 10 weeks for his science project he made a graph that shows how much the plant group e
vazorg [7]

Answer:

y= 6/5x + 2

If you substitute the points (5,8) you get:

8 = 6/5 × 5 + 2

8 = 6 + 2

Step-by-step explanation:

5 0
3 years ago
Write the equation of the line in slope-intercept form with slope m=4 through the point (-2,5)
wlad13 [49]

Answer:

y=4x+13

Step-by-step explanation:

Ig, hope it helps

5 0
2 years ago
How do I solve and graph this
White raven [17]
I hope this helps you out

5 0
3 years ago
Other questions:
  • the question is on the photo everything you guys need to know is there pls help me or I won't be able to turn in my homework.Thx
    10·1 answer
  • If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalen
    12·1 answer
  • A dime has the same value as 10 pennies Marley brought 290 pennies to the bank how many dimes did Marley get
    14·2 answers
  • Find the x-intercept of the graph of the function y=3/2x-6
    9·1 answer
  • Does (-8,-8) make the equation y = x true
    7·2 answers
  • 18.<br> Place parentheses in the following equation to<br> make it true.<br> 4 + 5 x 3-8 = 19
    6·1 answer
  • Frank builds a triangle from three pieces of drinking straws. Which lengths of straw
    14·1 answer
  • Add one set of parentheses to the expression 2x² + 4 - 5 so that the value of the expression is 75 when x = 6
    10·1 answer
  • Based on a table provided in your reading material, determine the monthly
    9·1 answer
  • According to this diagram, what is tan 62°?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!