Probability question:
a scientist finds 6 rare plants that can potentially cure a disease. he knows that only half of these plants are the right ingredients he needs and the rest have no effect on the disease. so, by mixing some or all of the plants, he prepares the most samples possible in order to find the right ingredients. the samples are prepared such that no two samples are similar in content and each one contains at least one of the right ingredients. then, for testing, he administers 1 sample to every individual in a group patients suffering from the disease, one by one. no sample is used more than once.
find the probability that at least one of the first 6 persons gets cured in the process.