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
HELP FAST FAST FAST FAST RIGHT NWOOWOWOW
Naily [24]
What do you need help with?
7 0
3 years ago
a pharmacist has 10 and 90 iodine solutions on hand. how many liters of each iodine solution will be required to produce 8 liter
Westkost [7]
1 litre of 10% solution contains 100mL of iodine
1 litre of 90% solution contains 900mL of iodine
Mixing them will produce 2 litres of solution containing 1000mL of iodine which is 50% iodine.
To produce 8 litres of 50% iodine they can mix 4 litres of 10% and 4 litres of 90%
6 0
2 years ago
What is 437 squared If you know please help me im doing exams Right now. Have a great day.
enyata [817]
190,969 should be the answer
4 0
3 years ago
Read 2 more answers
Diego is solving this system of equations:
USPshnik [31]

The solutions of the equations are x = 1 and y = 2

The system of equations are

4x + 3y = 10

-4x + 5y = 6

Here we have to use the elimination method. Eliminate the x term and find the value of y term

Add both equation

3y + 5y = 10 +6

Add the like terms

8y = 16

y = 16 / 8

Divide  the terms

y = 2

Substitute the value of x in the first equation

4x + 3y = 10

4x + 3×2 =  10

Multiply the terms

4x + 6  = 10

4x = 10 - 6

4x = 4

x = 4 / 4

Divide the terms

x = 1

Hence, the solutions of the equations are x = 1 and y = 2

Learn more about elimination method here

brainly.com/question/14619835

#SPJ1

7 0
1 year ago
EXERCÍCIOS 01) Resolva. A Lino tinha R$430,00 para pagar as seguintes contas R$ 119,00 de energia elétrica, R$65,00 de água e RS
satela [25.4K]

Answer:

$149

Step-by-step explanation:

The computation of the amount left for the shopping is shown below;

= Amount have - Electricity bill - Water bill - telephone bill

= $430 - $119  - $65 - $97

= $149

We simply deduct all expenses from the amount available so the remaining amount i.e. left would be considered for shopping

4 0
3 years ago
Other questions:
  • Graph the line.<br> y+2=-1/(x-1)
    15·1 answer
  • Someone Please Help with these questions, also it has to be solved for x Really need help I'm slow when it comes to math.
    9·1 answer
  • How would you explain this ?
    8·1 answer
  • How to read fraction 1/10 three ways
    11·1 answer
  • Support requests arrive at a software company at the rate of 1 every 30 minutes. Assume that the requests arrive as events in a
    15·1 answer
  • A motorbike travels 45 miles in 15 minutes, what is its speed ???? help ASAP please
    8·2 answers
  • Example 2<br> Let f(x) = 3x2 - 1. Find each of the following<br> a. f(9)<br> b. f(-2)<br> HELP PLS
    11·2 answers
  • Simplify the expression<br> 1/2x+3-1/4x-3
    5·1 answer
  • Find the domain and range of the function. ​f(x)=24+x^2
    14·1 answer
  • 1.rani was selling flowers. each day she made 7 bouquets by arranging 8 roses and 6 marigolds in each bouquet. each bouquet was
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!