1. 35% of glasses are tall, and the other 65% are short. In a durability test, 2
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Question
1. 35% of glasses are tall, and the other 65% are short. In a durability test, 20% of the tall glasses will develop imperfections, and 32% of the short glasses will develop imperfections. What percentage of the glasses with imperfections are tall?
2. A man goes to work either in his car, on a bus, or on a train. When he takes the car he is late 50% of the time; he is late 18% of the time on the bus; and he is late 8% of the time on the train. He drives his car to work 22% of the time, rides the bus 60% of the time, and takes the train 18% of the time. Given that he is late today, what is the probability that he rode the bus?
3. The rate of depression in America is about 6%, and the rate of anxiety in America is 18% (from www.webmd.com). A depressed American has an 85% chance of also having anxiety problems (from www.healthyplace.com). Find the chance that an American with anxiety problems is also depressed.
Explanation / Answer
1)
TOTAL TALL GLASS = 35% = 0.35
TOTAL SHORT GLASS = 65% = 0.65
IMPERFECTION IN TALL = 20% = 0.2
IMPERFECTION IN SHORT = 32% = 0.32
TOTAL IMPERFECTION IN ALL GLASS WILL BE 0.35*0.2 + 0.65*0.32 = 0.278
HENCE 27.8%
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