[Hypothetical Numerical Problem] In a city far far away, on Valentine's day, many people celebrate by having dinner in a nice restaurant. Approximately, 30% of women and 20% of men will have such a Valentine's day dinner. 40% of women who go to such a nice dinner will also prepare a gift and 90% of men will prepare a gift. What proportion of this city's women are who go to Valentine's day dinner without a gift?
I have been trying to understand this question but unable to get it. what i understand is that 50% is the sample space S. I think i need to find the conditional probability of women given without gifts. probability of without gift will be calculated by doing 1-P(gifts). I am really lost on this problem. Please help me better understand it.
Ps: The answer to this question is 18%
Best Answer
It's a super clear and easy question. 30% of city's women go to the party, and 40% of these women who are going there have prepared a gift as well. So 100%-40% of 30% of women of the city are going there without preparing any gift. 60% of 30% is $$0.6\times 0.3=0.18$$ which means 18%.
The information about men is just an extra information which is not going to be used in this question.