A researcher tracked a group of 900 high school students taking standardized tests in math and chemistry. Some of the students were given after-school tutoring before the tests (in both subjects) and the rest of the students received no tutoring. The following information is known about the test results:
- 510 of the students passed math test and 475 of the students passed chemistry test.
- Of the students who failed both subjects, there were 20% more students who did not receive tutoring than there were students who received tutoring.
- Of the students who failed chemistry and had tutoring, there were 99 more students who failed math than there were students who passed math.
- Of the students who failed chemistry and had no tutoring, there were 4 more students who failed math than there were students who passed math.
- There were 126 students who failed math and passed chemistry.
- 249 students passed math and had received no tutoring.
Determine the probability that a randomly selected student from this group had tutoring given that the student passed both subjects.
An insurance company tracked a group of 800 insureds for 2 years. It was found that 560 of the insureds had no claims in year 1 and 380 of the insureds had no claims in year 2. Of the insureds who had no claims in both years, there were four times as many male insureds than there were female insureds. Furthermore, there were 230 male insureds who had no claims in year 2 and there were 53 females insureds who had claims in both years. It is also known that there were 85 male insureds who had claims in year 1.
Determine the number of insureds who had no claims in year 1 but had claims in year 2.
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