1. Question Two [25 Marks]

a. Due to COVID-19 pandemic, the South African government is awarding students with bursary and daily free meals. Government had subjectively estimated that each student has a 70% probability of being approved to receive a bursary and a 67% probability of being approved to receive daily free meals if the applicant obtains bursary. If the application to receive a bursary was rejected, there is 50% probability of getting approval to receive daily free meals. Find the probability of an applicant getting approval to receive a bursary given that approval was already given for daily free meals. [15]

b. KZY Farms is located some 200 km from Durban. The farm rears cattle, chicken and pigs. There have recently been an outbreak of a bacteria disease within the piggery section of the farm. It has been estimated that the probability of finding a pig which would test positive to the bacterial infection is 30%. Calculate the number of pigs that would have to be tested if a laboratory technologist would be 99% sure of getting at least one positive result. [10]

1. Question Three [25 Marks] [25 Marks]

a. The random variable Y is B (3, 0.7). Construct the probability distribution for X and find the mean and standard deviation. [15]

b. Suppose X follows a Poisson distribution with standard deviation of 2.5. Find P(X=5). [10]