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Vandaag is het 30 September 2020

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# Also having birthday today? - math puzzle

Difficulty:   Rating: 2.1/5.0

 Out of how many people should a group at least consist in order to have that the probability that two persons out of that group are having birthday on the same day, is larger than 1/2? # 2=1? - math puzzle

Difficulty:  Rating: 2.3/5.0

Suppose: a = b

It then follows that
a * a = a * b
a^2 = a * b
a^2 - b^2 = a * b - b^2
(a - b) * (a + b) = (a - b) * b
a + b = b
a + a = a
2 * a = 1 * a
2 = 1

Is this derivation really correct? Or is there somewhere a mistake? If so, where?

# Infected? - math puzzle

Difficulty:    Rating: 2.4/5.0

 Suppose that 1 out of 1000 people of a specific country are infected with the deadly X-virus. An inhabitant of that country goes the hospital and gives some blood for a survey. Her blood is checked on the X-virus by a test which gives a correct outcome in 99% of the cases. The test points out that the woman is infected. After the investigation, a doctor tells the woman that he is 99% sure that she is infected with the X-virus. Can the doctor be right by making this worrying statement? 