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A boy may get a gift between $20 and $50 from his father with a probability of 95%, and he may also get a gist between $40 and $60 from his mother with a probability of 95%. What is the probability that the boy can receive his gift between $60 and $90?
Very bad question. Distributions are not specified. Also, the question is phrased oddly. His ability to receive has nothing to do with his parents' potential to give.
What we KNOW is that there is a 95% chance of between 20+40 and 50+60. Are we getting anywhere?
edit: removed post, i misread the question.
The problem was rephrased. The boy will definitely receive money from both his father and mother. We know that the probability of getting $20-$50 from his father is 95% and that the probability of getting $40-$60 from his mother is also 95%. The distribution information and the probability of getting other amount are unknown. What is the probability that the boy can receive something between $60 and $90? Is it greater than or equal to 95%? Or can we only know for sure is that the probability is >=95%*95?
We can say a little about 60-110, but not much about anything else.