In a murder trial in Los Angeles, the prosecution claims that the defendant was

Question

In a murder trial in Los Angeles, the prosecution claims that the defendant was cut on the left middle finger at the murder scene, but the defendant claims the cut occurred in Chicago, the day after the murders had been committed. Because the detendant is a sports celebrity, many people noticed him before he reached Chicago Twenty-two people saw him casually, one person on the plane to Chicago caretully studied his hands looking tor a championship ring, and another person stood him as he signed autographs and drove him from the airport to the hotel. None of these 24 people saw a cut on the defendant's finger. If in fact he was nol cut at all, it would be extremely unlikely that he let blood at the murder scene. a) Because a person casualy meeting the defendant would not be looking for a cut, assume that the probablity is o.7 that such a person would not have seen the cut, even if t was there Furthermore, assume thathe person who carefully looked the t defendant's hands had a 0.4 probability of not seeing the cut even if it was there and that the person who drove the defendant from the airport to the hotel had a 0.6 probability of not seeing the cut even if it was there. Given these assumptions,i also assuming that all 24 people looked at the detendant independently of each other, what is the probability that none of the 24 people would have seen the cut, even it it was there?(Do not round intermediate calculations and round your final answer to 4 decimal places.) Probability (b) What is the probabiny that at least one of the 24 people would have seen the cut it it was there? (Round your answer to 4 decimal places.) (c) Given the result of part b and given the fact that none of the 24 peaple saw a cut, do you think the defendant had a cut on his hand before he reached Chicago? No

Explanation / Answer

a)P( none of the 24 people had seen the cut even if it was there) = 0.7^22 * 0.4*0.6=0.000093

b)

P( All of the 24 people has seen the cut even if it was ther) = (0.3^22* 0.6*0.4=0.0000000000753

P( At least one had seen the cut) = 1-0.000093-0.000000000753=1

P( at least one person seeing the cut even if it was there) is approvimately 1 . Hence, the defendanet did not have a cut on his hand before he reached Chicago. Hence, the answer is NO

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