Question

FILE TOOLS VIEW May 2017_FE [Compatibility Mode] - Word (Product Activation Failed) - i. Find the probability that both A and B occur. [2 marks] 2. a. A survey of 100 small businesses classified based on profitability of the business and year of experience in that business. Table Q2a shows the following events: ii. Find the conditional probability that A will oc- cur given that B has occurred. [3 marks] A. The business is profitable iii. Find the probability that A will not occur. [2 marks] B. The business has been in existence for more than 5 years. iv. Find the probability that either A or B occur. [3 marks] TABLE Q2a: Results of profitability survey Profitability / Length of time Length of time in business in years Less 2-5 More Total than 2 than 5 24 16 43 100 14 Profitable Unprofitable Total 25 76 39

Answer 1

į. The probability is calculated as follows: 24 p(BothOccur) = 100 390.0936 100 Therefore, the probability that both occur is 0.0936. ii. The probability is calculated as follows: p(4|B) = 14 = 0.14 Therefore, the probability that A will occur given that B has occurred is 0.14. iii. The probability is calculated as follows: p(AC) = 1- 100 = 0.76 Therefore, the probability that A will not occur is 0.76. iv. The probability is calculated as follows: p(AOrB)=P(A)+p(B)-( A B ) 24 39 24 39 100 100 100 100 =0.5364 Therefore, the probability that A or B will occur is 0.5364. Good luck with your studies!!!