Question

Based on experience, the probability that an incoming email is spam (an undesired message of solicitation) is 38%. If three emails are in my inbox, what is the probability that:A. All three messages are spam.B. At least one of the three messages are spam.C. None of the three messages are spam.

Answer 1

0.0549

0.7617

0.2383

Explanation:

Given that:

Probability that incoming email is spam ;

P(spam) = 0.38

If three emails are in my inbox, what is the probability that:

A. All three messages are spam.

P(1st message being spam) * p(second message being spam) * p(3rd message being spam)

= (0.38) * (0.38) * (0.38)

= 0.054872

= 0.0549

B. At least one of the three messages are spam.

1 - p(none of the 3 messages are spam)

P(none of the 3 messages are spam)

P(not spam) = 1 - p(spam) = 1 - 0.38 = 0.62

1 - [P(not spam) * p(not spam) * p(not spam)]

1 - (0.62 * 0.62 * 0.62)

= 1 - 0.238328

= 0.761672

= 0.7617

C. None of the three messages are spam.

P(not spam) = 1 - p(spam) = 1 - 0.38 = 0.62

P(not spam) * p(not spam) * p(not spam)

(0.62 * 0.62 * 0.62)

= 0.238328

= 0.2383