1. A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major. Selected Major Gender Management Marketing Others Total Male 40 10 30 80 Female 30 20 70 120 Total 70 30 100 200 a. What is the probability of selecting an individual who is majoring in Marketing? b. What is the probability of selecting a female? c. What is the probability of selecting a female who is also majoring in Management? d. What is the probability of selecting an individual who is majoring in Management, given that the person is female? 2. If X and Y are mutually exclusive events with 0.295 = )?0(70.32 = )?0(7chen )? | 20(20 = 3. Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships (that is, the merit scholarship or the athletic scholarship or both) is 0.3. a. What is the probability that you will receive a Merit scholarship? b. Are events A and M mutually exclusive? Why or why not? Explain using probabilities . What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? 4. As a company manager for Rob Dem Blind Supermarket there is a 40% chance that you will be promoted this year. There is also 57% chance that you will get a raise this year. More than this, there is 25% of getting a promotion and a raise. a. Given that you get a promotion, what is the probability that you also get a raise