The table below shows the results of a survey that asked 2861 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (d).
$\begin{array}{rcccc} & \text { Frequently } & \text { Occasionally } & \text { Not at all } & \text { Total } \\ \text { Male } & 228 & 455 & 796 & 1479 \\ \text { Female } & 206 & 430 & 746 & 1382 \\ \text { Total } & 434 & 885 & 1542 & 2861\end{array}$
$P$ (being frequently involved or being occasionally involved $)=0.461$ (Round to the nearest thousandth as needed.)
(b) Find the probability that the person is female or not involved in charity work at all.
$P($ being female or not being involved $)=0.761$
(Round to the nearest thousandth as needed.)
(c) Find the probability that the person is male or frequently involved in charity work.
$\mathrm{P}($ being male or being frequently involved $)=$
(Round to the nearest thousandth as needed.)
Answer
Final Answer: The probability that the person is male or frequently involved in charity work is approximately \(\boxed{0.589}\)
Step 1 ：Given the total number of people surveyed is 2861, the total number of males is 1479, the total number of people frequently involved in charity work is 434, and the number of males frequently involved in charity work is 228.
Step 2 ：Calculate the probability of a person being male, which is the number of males divided by the total number of people. \(P(\text{Male}) = \frac{1479}{2861} = 0.517\)
Step 3 ：Calculate the probability of a person being frequently involved in charity work, which is the number of people frequently involved divided by the total number of people. \(P(\text{Frequently Involved}) = \frac{434}{2861} = 0.152\)
Step 4 ：Calculate the probability of a person being a male and frequently involved in charity work, which is the number of males who are frequently involved divided by the total number of people. \(P(\text{Male and Frequently Involved}) = \frac{228}{2861} = 0.080\)
Step 5 ：Calculate the probability of a person being male or frequently involved in charity work using the formula \(P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)\). Substituting the calculated probabilities, we get \(P(\text{Male or Frequently Involved}) = 0.517 + 0.152 - 0.080 = 0.589\)
Step 6 ：Final Answer: The probability that the person is male or frequently involved in charity work is approximately \(\boxed{0.589}\)
