A test for a particular illness that affects 8% ofthe general population has the following properties: - The test will show a positive in 98% of cases where the patient has the illness and a negative in 2% of such cases. - The test will show a false positive in ?% of patients who do not have the illness and a negative result for 93% of patients who do not have the illness. Note that a positive result means that the test indicates that the patient has the illness. A negative result means that the test indicates that the patient doesn't have \"die illness. A patient has just been tested and shows a positive result. Assuming all other things being equal. and based on the above information, nd the probability that the patient does not have the illness. Eive your answer as a decimal to 2 decimal places. Probability that patient does not have illness = \\:| An administIator who works at a tIain station has to monitor the drinks vending machine. when the machine gets low on stock, a warning light appears and the administrator is meant to contact the drinks supplier to rell the machine. However, the light is not always accurate. In particular, it will occassionally come on even when the stock is not low. The administrator knows the following probabilities: - On average the vending machine is low on stock on 2 out of every 100 days. That is, the probability of the vending machine being low on a random day is 0.02. - The warning light is very accurate when it comes to positively reporting low stock. Specically, if the stock is lowr the probability that the warning light will come on is 1. - However, the warning light also occasionally comes on even if the stock is not low although this is rare. The probability that the light will come on during the day when the stock isn't low is 0.001. The administIator notices that the light has just appeared on the machine. Based on this information, calculate the probability that the stock is not low in the machine given that the warning light has just come on. Give your answer as a decimal to 3 decimal places. P{stock is not lowlwaming light is on) = \\:| In the Legal Eagle law rm, 22% ofthe lawyers are male while 28% are female. ofthe male lawyers, 40% are corporate lawyers. of the female lawyers, 29% are corporate lawyers. If a corporate lawyer is chosen at random, calculate the probability that they are male. Give your answer as a decimal to 2 decimal places. probability = E