Of one hundred students surveyed: 70 like

basketball, 52 like football, 61 like baseball, 29 like
baseball and football, 39 like football and
basketball, 42 like basketball and baseball, 27 like
all three sports. If a student is chosen at random,
what is the probability that she/he likes no more
than one sport

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To find the probability that a randomly chosen student likes no more than one sport, we need to calculate the number of students who like either no sport or just one sport, and divide it by the total number of students surveyed.

To calculate this, we can use the principle of inclusion-exclusion. We start by summing the number of students who like each sport individually: 70 (like basketball) + 52 (like football) + 61 (like baseball).

Next, we subtract the students who like two sports: 29 (like baseball and football) + 39 (like football and basketball) + 42 (like basketball and baseball).

However, when we subtracted the students who like two sports, we also subtracted the students who like all three sports twice. Therefore, we need to add them back once: + 27 (like all three sports).

So, the number of students who like no more than one sport is: 70 + 52 + 61 - 29 - 39 - 42 + 27 = 100.

Finally, we divide the number of students who like no more than one sport by the total number of students surveyed (100) to get the probability: 100/100 = 1.

Therefore, the probability that a randomly chosen student likes no more than one sport is 1 or 100%.