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
yan [13]
3 years ago
13

I need help on this one.

Mathematics
1 answer:
Firlakuza [10]3 years ago
3 0

Answer: 1/3

Step-by-step explanation:

You might be interested in
Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o
myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is p = \frac{1}{5} = 0.2

10 questions.

This means that n = 10

A) What is the probability that he will answer all questions correctly?

This is P(X = 10)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so P(X = 0)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

P(X \geq 1) = 1 - P(X = 0)

Since P(X = 0) = 0.1074, from item b.

P(X \geq 1) = 1 - 0.1074 = 0.8926

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264

P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055

P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008

P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001

P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0

P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0

So

P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0
3 years ago
The sum of eight times a number and fifteen is seven
asambeis [7]
8x+15=7

In the statement the phrase the sum of can tell you that it is going to be an addition problem. So 8x ( eight times a number) would be added to the 15, 8x+15. Since its an addition problem the part where it says ' ... is seven', you know that it will all equal 7. So the answer would be 8x+15=7.
3 0
2 years ago
The area of this rhombus is 1 square millimeter. One of its diagonals is 1 millimeter.
aleksklad [387]

Answer:

yo momma

Step-by-step explanation:

7 0
3 years ago
A cylindrical glass is 40% full of liquid. If the base of the glass has a radius of 5 inches and the height of the glass
Elan Coil [88]

40

100

or the decimal 0.40. Notice that 80 out of 200 and 10 out of 25 are also 40%, since  

80

200

=

10

25

=

40

100

5 0
2 years ago
Please help meeeee. I literally learned this last year but my dum mb self forgot hot to do it
Aleks [24]

It would be 30 because 10^4 is 10000 and 10000 times 12 is 120000 and 10^3 is 1000 and 1000 times 4 is 4000 so 120000 divided by 4000 is 30

8 0
3 years ago
Other questions:
  • Ila invested $42,000 into an account earning 4% compounded annually. She makes no other deposits and does not withdraw any money
    15·1 answer
  • Working​ together, two people can cut a large lawn in 44 hr. One person can do the job alone in 1 hr less than the other. How lo
    15·1 answer
  • Solve the inequality showing all steps needed to justify your answer. State your solution in interval notation
    12·1 answer
  • The two bases of a trapezoid are 3 and 11 and the altitude is 8 . What is the area of the trapezoid?
    15·1 answer
  • The sum of two fractions is 31/4 if one of them is 17/6 find the other
    9·1 answer
  • Find the measure of the incanted angle to the nearest degree
    10·2 answers
  • I don't understand this. Plz help!!!
    13·2 answers
  • How do you solve this?
    15·1 answer
  • Question below..................
    13·1 answer
  • What equation results from completing the square and then factoring?<br> x2 + 10X = 15
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!