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.

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.
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Solution

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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. $P(\text{Important}) = P(\text{Important Text}) + P(\text{Important Email}) = 0.272 + 0.136 = 0.408$

Final Answer: The final answer is $\boxed{0.408}$

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