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
Leya [2.2K]
3 years ago
7

Suppose that you are given a bag containing n unbiased coins. You are told that n-1 of these coins are normal, with heads on one

side and tails on the other, whereas one coin is a fake, with heads on both sides. Suppose you reach into the bag, pick out a coin at random, flip it, and get a head. What is the (conditional) probability that the coin you chose is the fake coin
Mathematics
1 answer:
gladu [14]3 years ago
5 0

Answer:

The (conditional) probability that the coin you chose is the fake coin is 2/(1 + n)

Step-by-step explanation:

Given

Total unbiased coin = n

Normal coins =n - 1

Fake = 1

The (conditional) probability that the coin you chose is the fake coin is represented by

P(Fake | Head)

And it's calculated as follows;

P(Fake | Head) = P(Fake, Head) ÷ P(Head) ----- (1)

Where P(Fake, Head) = P(Fake) * P(Head | Fake)

P(Fake) = 1/n --- because only one is fake

P(Head | Fake) = n/n because all coins (including the fake) have head

So, P(Fake, Head) = P(Fake) * P(Head | Fake) becomes

P(Fake, Head) = 1/n * n/n

P(Fake, Head) = 1/n

P(Head) is calculated by

P(Fake) * P(Head | Fake) + P(Normal) * P(Head | Normal)

P(Fake) * P(Head | Fake) = P(Fake, Head) = 1/n (as calculated above)

P(Normal) * P(Head | Normal) = ½ * (n - 1)/n ----- considering that the coin also has a tail with equal probability as that of the head.

Going back to (1)

P(Fake | Head) = P(Fake, Head) ÷ P(Head) becomes

P(Fake | Head) = (1/n) ÷ ((1/n) + (½(n-1)/n))

= (1/n) ÷ ((1/n) + (½(n-1)/n))

= (1/n) ÷ (1/n + (n - 1)/2n)

= (1/n) ÷ (2 + n - 1)/(2n)

= (1/n) ÷ (1 + n)/(2n)

= (1/n) * (2n)/(1 + n)

= 2/(1 + n)

Hence, the (conditional) probability that the coin you chose is the fake coin is 2/(1 + n)

You might be interested in
The ratio of the areas of the two squares is 25 to 9. The side length of the smaller square is 30 meters. How long is the side l
Ratling [72]
Ratios of Area of the two squares = 25:9
So then let the areas be A1 = 25A and A2 = 9A, A is common element
Side of the smaller area S2 = 30 meters
Area of the smaller square A2 = 30 x 30 = 900
We have area of smaller square as 9A = 900 => A = 100
Area of the large square = 25A = 25 x 100 = 2500.
Hence S1^2 = 2500 => S1 = 50 meters which is 20 meters longer than the
side of the smaller square.
6 0
2 years ago
Find the measurement of angle b
Anuta_ua [19.1K]

Answer:

133

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Choose an integer between -5 and -10. Label it ܴ on the number line created in Problem 3, and complete the following tasks.
qwelly [4]

Answer:

Your search - Choose an integer between -5 and -10. Label it ܴ on the number line created in Problem 3 ... - did not match any documents.

Suggestions:

Make sure all words are spelled correctly.

Try different keywords.

Try more general keywords.

Try fewer keywords.

Step-by-step explanation:

6 0
2 years ago
What is a polygon with four right angles and four sides
german

a square ///////////

4 0
3 years ago
Read 2 more answers
Simplify the expression.<br> <img src="https://tex.z-dn.net/?f=%28%5Cfrac%7B15y%5E5%7D%7B3y%5E2%7D%20%29%20%5E2" id="TexFormula1
Olenka [21]
Use a all called math w.a.y (remove the periods) trust me it helps with at least 75% of math problems
7 0
2 years ago
Other questions:
  • Choose the best definition for the term: variable
    5·1 answer
  • How do i find the volume of a sphere radius 1/2
    10·1 answer
  • If (x-10) is a factor of the polynomial P(x), which of the following do we know to be true?
    13·2 answers
  • A cylindrical grain silo is being built for Mr. Greenjeans. The silo is 13 meters tall with a diameter of 6 meters. If the entir
    9·1 answer
  • A starting carpenter can build a rough table in 1 hour, and a rough chair in 45 minutes. A finishing carpenter can finish each t
    13·1 answer
  • What is the volume for the cone
    9·2 answers
  • Step by step how to do 4 divided by 2/3.
    11·2 answers
  • You ride through some wet paint on your bike, creating a red spot on the tire. Write a cosine equation to model the height of th
    10·1 answer
  • The notes say that the Continental Congress created a committee to write a plan for government. Based on the notes, whom did the
    10·1 answer
  • A pack of cookies contains 24 cookies. Now the advertisement says that the pack contains 25% more then before How many cookies a
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!