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
lawyer [7]
3 years ago
11

Jane must get at least three of the four problems on the exam correct to get an A. She has been able to do 80% of the problems o

n old exams, so she assumes that the probability she gets any problem correct is 0.8. She also assumes that the results on different problems are independent. (a) What is the probability she gets an A? (b) If she gets the first problem correct, what is the probability she gets an A?
Mathematics
1 answer:
NISA [10]3 years ago
3 0

Answer:

a) There is n 81.92% probability that she gets an A.

b) If she gets the first problem correct, there is an 89.6% probability that she gets an A.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the answer is correct, or it is not. This means that we can solve this problem using binomial distribution probability concepts.

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}.\pi^{x}.(1-\pi)^{n-x}

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

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

And \pi is the probability of X happening.

For this problem, we have that:

The probability she gets any problem correct is 0.8, so \pi = 0.8.

(a) What is the probability she gets an A?

There are four problems, so n = 4

Jane must get at least three of the four problems on the exam correct to get an A.

So, we need to find P(X \geq 3)

P(X \geq 3) = P(X = 3) + P(X = 4)

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

P(X = 3) = C_{4,3}.(0.80)^{3}.(0.2)^{1} = 0.4096

P(X = 4) = C_{4,4}.(0.80)^{4}.(0.2)^{0} = 0.4096

P(X \geq 3) = P(X = 3) + P(X = 4) = 2*0.4096 = 0.8192

There is n 81.92% probability that she gets an A.

(b) If she gets the first problem correct, what is the probability she gets an A?

Now, there are only 3 problems left, so n = 3

To get an A, she must get at least 2 of them right, since one(the first one) she has already got it correct.

So, we need to find P(X \geq 2)

P(X \geq 3) = P(X = 2) + P(X = 3)

P(X = 2) = C_{3,2}.(0.80)^{2}.(0.2)^{1} = 0.384

P(X = 4) = C_{3,3}.(0.80)^{3}.(0.2)^{0} = 0.512

P(X \geq 3) = P(X = 2) + P(X = 3) = 0.384 + 0.512 = 0.896

If she gets the first problem correct, there is an 89.6% probability that she gets an A.

You might be interested in
65 Divided by 3459 what is it?
telo118 [61]

Answer: 53.2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Please help I will mark brainlist if correct
djyliett [7]
Solving for L:

P = 2L + 2W
P - 2W = 2L
(P - 2W) / 2 = L
L = (P - 2W) / 2
8 0
3 years ago
Which equation is the Pythagorean theorem
lisov135 [29]

Answer:

B

Step-by-step explanation:

6 0
3 years ago
How many 2/3s are in 3
ale4655 [162]

Answer:

7 and 1/3

Step-by-step explanation:

5 0
3 years ago
Rewrite the equation below so that it does not have fractions.
Eduardwww [97]

Answer:

6x-40=3

Step-by-step explanation:

3/4 x -5 =3/8

Multiply each side by 8 to get rid of the fractions.

8(3/4x -5 ) =8*3/8

Distribute

6x-40=3

5 0
2 years ago
Read 2 more answers
Other questions:
  • A Company increased the number of its employees from 340 to 425. Find the percent increase.
    9·1 answer
  • Last question helo me pls
    12·1 answer
  • Which expression represents the perimeter of the rectangle with a width of 4x+3 and legnth of 2x?
    10·1 answer
  • abby makes two different quilts. Each quilts is a square. However, the quilts have diferent perimeter, and areas. Describe the a
    11·2 answers
  • The integer between - 2.8 and -1.4 is<br> .<br> Check
    9·2 answers
  • If a loaf of bread was priced $1.50 on one day and $1.20 the next, what is the percent decrease
    14·1 answer
  • Express 6 hours as a percentage of 2 days (Part)​
    5·1 answer
  • What is the equation of the line that passes through the points (5,-6) and (-9. 10) ? Write the equation in point-slope form.​
    15·1 answer
  • Pls help! <br><br> substitute x = 2 and y = 4 into the following and evaluate.<br> 12/x + 10xy/2
    15·1 answer
  • Question 3 (1 point) If the following is a rhombus, find the missing measures. Find PQ. PQ=​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!