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Alex receives 55 emails a day. Out of the 55 emails, 12 emails are spam. If Alex opens 6 emails at random, what is the probability that none of the emails are spam? Enter your answer in decimal form rounded to the nearest thousandths.

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He receives 55 emails. Out of the 55 emails, 12 emails are spam. He opens 6 emails at random. The probability that none of the mails are spam can be calculated as follows

emails that are not spams = 55 - 12 = 43 emails

[tex]\frac{43}{55}\times\frac{42}{54}\times\frac{41}{53}\times\frac{40}{52}\times\frac{39}{51}\times\frac{38}{50}=\frac{4389446880}{20872566000}=0.21029742485\approx0.210[/tex]