ABT Mining is about to perform a detailed geologic analysis at a site that preliminary tests indicate is 60% likely to contain a signifcant vein of silver. The detailed geologic analysis will be used to further assess the chances that a signifcant vein of silver will be found at the site. The detailed analysis will give one of four readings: strong positive, strong negative, weak positive, or weak negative. Based on previous experience with the test, if a site contains a signifcant vein of silver, it’s 56% likely that the analysis will give a strong positive reading, 31% likely that it will give a weak positive reading, 9% likely that it will give a weak negative reading, and 4% likely to give a strong negative reading. If a site doesn’t contain a significant vein of silver, the analysis is still 2% likely to give a strong positive reading, 13% likely to give a weak positive reading, 38% likely to give a weak negative reading and 47% probability of giving a strong negative reading.
a. If the analysis gives a “strong positive” result, how likely is it that the site actually has a signifcant vein of silver?
b. If the analysis gives a “weak negative” result, how likely is it that the site actually has a signifcant vein of silver?
c. If the analysis gives a “strong negative” result, how likely is it that the site does not have a signifcant vein of silver?