Question

DEPENDENT EVENTS AND CONDITIONAL PROBABLYAlex 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? Round to the nearest thousandths.

Answer 1

Given:

Number of mails received a day = 55

Spam mails = 12

Alex opens 6 emails at random.

Number of emails that are not spam = 55 - 12 = 43

The probability that none of the emails are spam is:

$P\text{ = }\frac{^{43}C_6}{^{55}C_6}$

Solving further, we have:

$P\text{ = }\frac{6096454}{28989675}\text{ = 0.210}$

Therefore, the probabilty that none of the emails are spam is 0.210

ANSWER:

0.210