Nepal has one of the highest mortality rate from giving birth in the world, and one main cause of that is because the mothers did not know they were pregnant until close to their due date. An NGO did research in Nepal on women's awareness about their pregnancy. They found and surveyed several women of age 18-35 in Nepal and asked them if they were pregnant at the time of the survey. 61% answered "not pregnant", 27% answered pregnant", and the rest answered "I don't know". Out the of ones that said they were not pregnant, 12% of them were actually pregnant at that time. Out of the ones who said they were pregnant, 1% of them were actually not pregnant. And out of the ones who answered "I don't know", 31% of them were actually pregnant at that time. (Use at least 4 decimal places when working this problem and assume 'woman' means woman surveyed as given above.)
1. What is the probability that a woman is actually pregnant at the time of the survey?
2. If we choose a woman who is actually pregnant, what is the probability that she said that she was wrong (not unsure) about her pregnancy status?
3. What is the probability that a woman was actually pregnant or reported being pregnant?
4. If we choose a woman who is actually not pregnant, what is the probability that she said she was pregnant?
5. What is the probability that a woman answered the survey correctly based on her pregnancy status at the time of the survey?