An individual has 3 different email accounts. Most of her messages, in fact 60% come into account #1, whereas 30%come into accou

Question

3 months ago

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An individual has 3 different email accounts. Most of her messages, in fact 60% come into account #1, whereas 30%come into accou

nt #2, and the remaining 10% into account #3. Of the messages into account #1, only 1% are spam, whereas the corresponding percentages for account #2 and #3 are 3% and 5%, respectively. What is the probability that a randomly selected message is spam?

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-03-29T00:18:28+03:00

Answer:

the likelihood is 0.02 (2%)

Step-by-step explanation:

let's define the event S as the message being classified as spam, thus the probability can be expressed as

P(S) = probability that a message picked at random originates from account #1 * probability that this message is spam given it came from account #1 + probability that a message picked at random originates from account #2 * probability that this message is spam given it came from account #2 + probability that a message picked at random originates from account #3 * probability that this message is spam given it came from account #3 = 0.6 * 0.01 + 0.3 * 0.03 + 0.1 * 0.05 = 0.02 (2%)

therefore, the probability is 0.02 (2%)