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aniked [119]
2 years ago
6

There are 12 of the zodiac. how many people are needed to guarantee that at least six of these people have the same sign? your a

nswer must be one integer.
SAT
1 answer:
ElenaW [278]2 years ago
6 0

Answer:es, the answer is 61. This is related to a mathematical principle called the Pigeonhole Principle, which states that if you are trying to sort  n+1  objects into k sets (where nk=r;n,k,r∈Z+), at least one set must contain at least r+1 objects. (This can be proven by proof by contradiction, but is pretty standard and so generally can just be used as justification of an answer by itself.)

For your problem, you have 12 signs of the zodiac - these are your 12 sets (so k=12). You are looking to find how many it takes before a set contains 6 objects (so r+1=6 and thus r=5). Therefore, n+1=r×k+1=12×5+1=61.

Explanation:

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What is the probability that a randomly chosen u. S. President is left-handed and a democrat?.
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Using conditional probability, it is found that there is a 0.052 = 5.2% probability that a randomly chosen U. S. President is left-handed and a democrat.

<h3>What is Conditional Probability?</h3>

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

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

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • P(A \cap B) is the probability of both A and B happening.
  • P(A) is the probability of A happening.

In this problem, the events are:

  • Event A: President is left-handed.
  • Event B: President is a democrat.

Researching the problem on the internet, it is found that:

  • 40% of the presidents were left-handed, hence P(A) = 0.4.
  • If a president is left-handed, there is a 13% chance that the president is a Democrat, hence P(B|A) = 0.13.

Then:

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

0.13 = \frac{P(A \cap B)}{0.4}

P(A \cap B) = 0.13(0.4)

P(A \cap B) = 0.052

0.052 = 5.2% probability that a randomly chosen U. S. President is left-handed and a democrat.

You can learn more about conditional probability at brainly.com/question/15536019

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