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
Marta_Voda [28]
3 years ago
11

An arcade booth at a county fair has a person pick a coin from two possible coins available and then toss it. If the coin chosen

lands on heads, the person gets a prize. One coin is a fair coin and one coin is a biased coin (unfair) with only a 32% chance of getting ahead. Assuming the equally likely probability of picking either coin, what is the probability that the fair coin is the one chosen, given that the chosen coin lands on heads?
a. 0.8300
b. 0.6024
c. 0.0149
d. 0.4150
e. 0.4310
Mathematics
1 answer:
nydimaria [60]3 years ago
7 0

Answer:

<em>b. 0.6024</em>

Step-by-step explanation:

<u>Conditional Probability</u>

Suppose two events A and B are not independent, i.e. they can occur simultaneously. It means there is a space where the intersection of A and B is not empty:

P(A\cap B) \neq 0

If we already know event B has occurred, we can compute the probability that event A has also occurred with the conditional probability formula

\displaystyle P(A|B)=\frac{P(A\cap B)}{P(B)}

Now analyze the situation presented in the question. Let's call F to the fair coin with 50%-50% probability to get heads-tails, and U to the unfair coin with 32%-68% to get heads-tails respectively.

Since the probability to pick either coin is one half each, we have

P(U)=P(F)=50\%=0.5

If we had picked the fair coin, the probability of getting heads is 0.5 also, so

P(F\cap H)=0.5\cdot 0.5=0.25

If we had picked the unfair coin, the probability of getting heads is 0.32, so

P(U\cap H)=0.32\cdot 0.5=0.16

Being A the event of choosing the fair coin, and B the event of getting heads, then

P(B)=P(F\cap H)+P(U\cap H)=0.25+0.16=0.41

P(A\cap B)=P(F\cap H)=0.25

\displaystyle P(A|B)=\frac{0.25}{0.41}=0.61

The closest answer is

b. 0.6024

You might be interested in
Elvin read 4/7 of the pages in his book. He has 226 pages left to read. How many pages has he read already?
Brut [27]

Answer:

he has read 129 pages


8 0
3 years ago
Sam wants to write an equation to represent a proportional relationship with a constant of proportionality of 6. He writes the e
vazorg [7]
<span>
</span>Sam wants to write an equation to represent a proportional relationship with a constant of proportionality of 6. He writes the equation y = 6 + x.
5 0
2 years ago
Read 2 more answers
Solve the equation 14=7(2x-4) using two different methods. Show your work. Which method do you prefer? Explain. need help thanks
Jet001 [13]

Answer:

x=3

Step-by-step explanation:

14=7(2x-4)

14/7=2x-4

2=2x-4

2x=2+4

2x=6

x=6/2

x=3

------------

14=7(2x-4)

14=14x-28

14x=14+28

14x=42

x=42/14

x=3

5 0
3 years ago
Read 2 more answers
Which ratio is equivalent to the scale 3 in. :1 ft?
poizon [28]

Answer:

4:1

Step-by-step explanation:

8 0
2 years ago
PLEASE ANSWERRRRRRRRRRRRRRRRRRRR
Tresset [83]

no solution

sorry its ins

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Krissy ran three miles one morning she ran the first mile in 11. 74 minutes the second mile in 11. 26 minutes in the third mile
    14·1 answer
  • A set of problems on Algebra, Geometry, and Combinatorics consists of 52, 70, and 88 problems. If 2 more problems from each cate
    6·2 answers
  • simplify the difference. (–7x – 5x4 5) – (–7x4 – 5 – 9x) a. 2x4 2x 10 b. –14x4 10x 10 c. –14x4 – 10x 10 d. 2x4 2x 8
    14·1 answer
  • CAN SOMEONE HELP
    14·2 answers
  • What does S in Math means?
    8·1 answer
  • Order the following numbers from least to greatest.<br> Put the least value on the left.
    12·2 answers
  • Can someone help me please? Quick.
    6·1 answer
  • rita swam 300 john swam 900 rodell swam 925 If the swimmers received $2 for every lap they swam, how much did each swimmer earn
    5·1 answer
  • 2. LUIS WANTS TO BUY 2 PENCILS AND 1 NOTEBOOK IN THE STORE. EACH PENCIL COSTS $2 AND THE NOTEBOOK COSTS $6. HOW MUCH MONEY DID L
    9·1 answer
  • Draw a model to represent 42/7
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!