1. What is the probability the person is frequently involved in charity work? Total of surveyed = 2850, Total number frequently participated in charity = 428, the probability of the person being frequently involved in charity work is 428/2850 = 0.150.
2. What is the probability the person is female and frequently involved in charity work? Total of surveyed = 2850, total number female participated in charity = 1378, the probability of the person being female and involved in charity work is 1378/2850 = 0.4835.
3. Given that the person is male, what is the probability that they are occasionally involved in charity work? Total of surveyed = 2850, total number male occasionally participated in charity = 456, the probability of the person being male and occasionally participating in charity work is 456/2850 = 0.1600.
4. What is the probability that the person is female, given that they are not at all involved in charity work? Total number of female not at all participated in charity = 741, the probability of the person being female and not at all participating in charity work is 741/2850 = 0.2600.
5. The probability a person at a particular school works full time is 22%. Three people are randomly selected from this school.
a) The probability that all three work full time is (0.22)^3.
b) The probability that none of the three work full time is (1-0.22)^3.
c) The probability that at least one of them works full time is 1 - (probability that none work full time).