Questions: The format and type of messages an individual gets for a month are related. Find the probability of selecting a message that is important.
Transcript text: The format and type of messages an individual gets for a month are related. Find the probability of selecting a message that is important.
Solution
Solution Steps
Step 1: Calculate the probability of important texts.
Multiply the probability of receiving a text by the probability that the text is important.
$P(\text{Important Text}) = P(\text{Text}) \times P(\text{Important } | \text{ Text}) = 0.32 \times 0.85 = 0.272$
Step 2: Calculate the probability of important emails.
Multiply the probability of receiving an email by the probability that the email is important.
$P(\text{Important Email}) = P(\text{Email}) \times P(\text{Important } | \text{ Email}) = 0.68 \times 0.20 = 0.136$
Step 3: Calculate the total probability of receiving an important message.
Add the probabilities of receiving an important text and an important email.
$P(\text{Important}) = P(\text{Important Text}) + P(\text{Important Email}) = 0.272 + 0.136 = 0.408$