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ElenaW [278]
3 years ago
13

Three Aztecs are dressing for a football game. They know there are 5 helmets in the locker, 3 black and 2 red. As they are about

to get their helmets, the lights go out. They all decide to just grab a helmet in the dark and head for the field. As they go in single file out into the tunnel, the one in the back says, "I can see both of the helmets in front of me, but I do not know the color of my helmet". The one in the middle says, "I can see the helmet in front of me, but I cannot determine the color of my own". The one leading the pack says, "I can see neither of the helmets behind me but I know the color of my own". How does he do it and what color was the helmet?
Mathematics
1 answer:
muminat3 years ago
4 0

We are given that there are:

Black helmets = 3

Red helments = 2

 

Let us start from the guy at the back. The guy at the back can see the two helmets in front of him. If the two helmets in front of him are red, then he can certainly say that his helmet is black since there are only 2 red helmets. Since that is not the case, then therefore he can either be black or red. Therefore this also means that at least 1 of the 2 guys in front of him has black helmet.

<span>Since the remaining two should have at least 1 black, therefore the middle guy can see that the helmet in front of him is not red (so 1st guy is black). Because if the guy in front of him is red, then he can know that he must be black since remember, at least one of the 2 front guys must be black, but the middle guy cannot say that. Therefore the 1st guy knows he has a black helmet.</span>

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T + V = 50

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y = -1/2 x - 3.5

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The prostate-specific antigen (PSA) test is a simple blood test to screen for prostate cancer. It has been used in men over 50 a
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The question is incomplete. I am writing the complete question below:

The prostate-specific antigen (PSA) test is a simple blood test to screen for prostate cancer. It has been used in men over 50 as a routine part of a physical exam, with levels above 4 ng/mL indicating possible prostate cancer. The test result is not always correct, sometimes indicating prostate cancer when it is not present and often missing prostate cancer that is present. Suppose that these are the approximate conditional probabilities of a positive (above 4 ng/ml) and negative test result given cancer is present or absent.

                                    Positive Result                 Negative Result

Cancer Present                   0.21                                       0.79

Cancer Absent                    0.06                                      0.94

In a large study of prostate cancer screening, it was found that about 6.6% of the population has prostate cancer.

What is the probability that the test is positive for a randomly chosen person from this population? (Enter your answer to five decimal places.)

P(Positive test) =

Answer:

P(Positive Result) = 0.0699

Step-by-step explanation:

We are given that 6.6% of the population has prostate cancer. So,

P(Cancer Present) = 0.066

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From the given conditional probability table, we have:

P(Positive Result | Cancer Present) = 0.21

P(Positive Result | Cancer Absent) = 0.06

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                             = 0.01386 + 0.05604

P(Positive Result) = 0.0699

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