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In a committee of 25 members each member is proficient either in mathematics or in its statistics or in both. If 19 of these are proficiant in mathematics, 16 in statistics. Find the probability that a person Select from the
committee is proficient in both.

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Detailed Solution

Let $A & B$ are the events that selected proficients in maths & satistics.

$P (A) = \frac{19}{25}; P (B) = \frac{16}{25}$

$P (A \cup B) = 1$

$P (A) + P (B) - P (A \cap B) = 1$

$P (A \cap B) = P (A) + P (B) - 1$

$\frac{19}{25} + \frac{16}{25} - 1 = \frac{19 + 16 - 25}{25}; = \frac{10}{25}$

$P (A \cap B) = \frac{2}{5}$

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