Question

An individual has four different email accounts. 60% of emails come into his corporate account,
30% come into his gmail account and the remaining 10% are equally divided into his yahoo and zoho accounts.
Only 1% of the emails in his corporate accounts are spam, whereas corresponding percentages for gmail, yahoo
and zoho accounts are 2%, 3% and 3%, respectively. Assuming that the same spam filter is used in all the four
email accounts, the probability (in percentage, rounded off to one decimal place) of having a randomly selected
email as spam is ____________.

Hint:

Use the law of total probability: weight of each account × its spam rate.

Answer 1

Correct Answer: 1.5

Weights of emails:
Corporate = 0.60, \qquad Gmail = 0.30, \qquad Yahoo = 0.05, \qquad Zoho = 0.05.
Spam rates:
Corporate = 1% = 0.01,
Gmail = 2% = 0.02,
Yahoo = 3% = 0.03,
Zoho = 3% = 0.03.
Total spam probability:
\[ P(\text{spam}) = 0.60(0.01) + 0.30(0.02) + 0.05(0.03) + 0.05(0.03). \]
Compute each term:
\[ 0.60(0.01) = 0.006,
0.30(0.02) = 0.006,
0.05(0.03) = 0.0015,
0.05(0.03) = 0.0015. \]
Add them:
\[ P(\text{spam}) = 0.006 + 0.006 + 0.0015 + 0.0015 = 0.015. \]
Convert to percentage:
\[ 0.015 \times 100 = 1.5%. \]
Thus, the final answer is:
\[ \boxed{1.5%} \]