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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

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Hope this helps!

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2 years ago
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If 24 marks is 60% what is full marks
Luda [366]

If 24 marks is 60 %, then full marks is 40

<em><u>Solution:</u></em>

Given that 24 marks is 60 %

We are asked to find the full marks

Let the full marks be "x"

So out of "x" marks, he has got 24 marks

Therefore,

60 % of full marks = 24

60 % of x = 24

60 \% \times x = 24\\\\\frac{60}{100} \times x = 24\\\\0.6x = 24\\\\x = \frac{24}{0.6}\\\\x = 40

Therefore, full marks is 40

<h3><u>Method 2:</u></h3>

If 60 % is 24, then we have to find what is 100 %

60 % = 24

100 % = x

This forms a proportion, So we can solve the sum by cross multiplying

60 \% \times x = 24 \times 100 \% \\\\60x = 2400\\\\x=\frac{2400}{60}\\\\x = 40

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

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2x-x=10-6\\ x=4


8 0
3 years ago
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