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
jek_recluse [69]
3 years ago
7

Assume that you have two dice, one of which is fair, and the other is biased toward landing on six, so that 0.25 of the time it

lands on six, and 0.15 of the time it lands on each of 1, 2, 3, 4 and 5. You choose a die at random, and roll it six times, getting the values 4, 3, 6, 6, 5, 5. What is the probability that the die you chose is the fair die? The outcomes of the rolls are mutually independent.
Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
5 0

Answer:

0.4038

Step-by-step explanation:

Let A and B be the events

A: “The die is fair”

B: “The die lands on 6 two times out of 6”

We want to determine if the die is fair given that it landed on 6 two times out of 6 tosses, that is P(A | B).

By the Bayes' theorem  

\large P(A|B)=\displaystyle\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^c)P(A^c)}

Where \large A^c is the event “the die is not fair”.

Since there are 2 dice,

\large P(A)=P(A^c)=1/2

If the die is fair P(B | A) is the probability of getting exactly two six in a binomial experiment with probability of “success” (land on 6) 1/6 and six repeated trials  

\large P(B|A)=\binom{6}{2}(1/6)^2(5/6)^4=0.2009

and \large P(B|A^c) is the probability of getting exactly two six in a binomial experiment with probability of “success” (land on 6) 0.25 and six repeated trials  

\large P(B|A^c)=\binom{6}{2}(0.25)^2(0.75)^4=0.2966

hence

\large P(A|B)=\displaystyle\frac{0.2009*0.5}{0.2009*0.5+0.2966*0.5}=0.4038

You might be interested in
Need help pls solve Find the area of the figure.
vampirchik [111]

Answer:

32 ft²

Step-by-step explanation:

Given the right angle and equal sides, we have a square. The diagonal is the hypotenuse of a right triangle, so we can use the Pythagorean Theorem to calculate the side lengths, or realize that the side lengths Squared will be the area of the square.

c² = a²+b² Since a² equals b², the equation becomes c² = 2a²

8² = 2a²

64/2 = a²

32 = a², the area of the square.

The side lengths of the square are √32

about 5.657 feet. If we square that square root, we get the area of the square, 32 square feet.

5 0
2 years ago
Bill Board is "lording" his SAT score over his friend, Rhoda Dendron, who took the ACT. "You only got a 25 in math," he chortled
SCORPION-xisa [38]

Answer:

Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score)  on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Bill:

Scored 300, so X = 300

SAT has a μ of 500 and a σ of 100.

His z-score is:

Z = \frac{X - \mu}{\sigma}

Z = \frac{300 - 500}{100}

Z = -2

Z = -2 has a p-value of 0.02.

This means that Bill, whose SAT score has Z = -2, scored in the 2nd percentile.

Rhoda

Scored 25, so X = 25.

ACT has a μ of 20 and a σ of 5

Her z-score:

Z = \frac{X - \mu}{\sigma}

Z = \frac{25 - 20}{5}

Z = 1

Z = 1 has a p-value of 0.84

This means that Rhoda, whose ACT score has Z = 1, scored in the 84th percentile.

What is wrong with Bill’s logic ?

Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score)  on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.

4 0
3 years ago
(-3,1) (-7,-2) <br> The slope is?
coldgirl [10]

Answer:

3/4

Step-by-step explanation:

Δy = y1 - y2 = 1 - (-2) = 3

Δx = x1 - x2 = -3 - (-7) = 4

Slope = Δy/Δx = 3/4

7 0
2 years ago
The range of y = Arcsin x is<br> kle<br> A. True<br> B. False
Yuri [45]

Answer:

I guess is

Step-by-step explanation:

False I guess

6 0
3 years ago
For what values of x will the result of 5x be greater than 1
SSSSS [86.1K]
Anything greater than (1/5) that is positive

Ex. (1/4), (1/3), (1/2), 1, 2, 3, 4, 5
6 0
2 years ago
Other questions:
  • a large tub of popcorn costs 3.80 and holds 200g a regular tub of popcorn costs 3.50 and holds 175g ,which is better value for m
    13·2 answers
  • A technician charges $25 per hour plus $50 for a
    5·1 answer
  • What is -3x6 with explanation
    8·2 answers
  • Mr. and Mrs. Jones wanted to plan a fun day with their two children. An adult ticket to the local amusement park is $20. A child
    5·2 answers
  • Which matrix represents the system of equations shown below?<br> 4x - 2y = 8<br> 2x-3y = 12
    10·1 answer
  • Need help hurry pleaseee !!
    11·2 answers
  • PROBLEM 1<br> What is the next term in the sequence -5, -1,3,7,...?
    15·1 answer
  • F(x) = 7x+2 what's the value of f(7)
    15·2 answers
  • The table shows the amount of money that Gabe earns based on the number of hours he works. Based on the table, which equation re
    14·1 answer
  • A baseball player makes 4 hits every 7 times at bat. At this rate, how many times did you hit if you hit 24 hits? 42 times 96 ti
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!