We can solve this problem using the principle of inclusion-exclusion. The total number of students is 30. Of these, 10 take Mathematics, 12 take English, and 5 take both Mathematics and English. The number of students who take either Mathematics or English is the sum of those who take Mathematics only, those who take English only, and those who take both Mathematics and English. So, Number of students who take either Mathematics or English = (10 - 5) + (12 - 5) + 5 = 17 Therefore, the number of students who take neither Mathematics nor English is: 30 - 17 = 13 So, the probability that a randomly chosen student takes neither Mathematics nor English is: 13/30 Therefore, the probability that the chosen student takes neither Mathematics nor English is 13/30.
