Professor Jackson is in charge of a program to prepare students for a high school equivalency exam. Records show that, in the program, 80% of the students need work in mathematics, 70% need work in English, and 55% need work in both areas. One person is to be randomly selected from this population of all students in the program. LetM = the selected person needs help in MathematicsE = the selected person needs help in EnglishThe probability that the selected person needs help in English and in Mathematics, i.e., P(E and M) is ______The probability that the selected person needs help in English or in Mathematics, i.e., P(E or M) is ______

Answer:P(E and M) = 55% = 0.55P(E or M) = 0.95 = 95%Step-by-step explanation:Percentage of students who need help in mathematics  = 80% = 0.80Percentage of students who need help in English  = 70% = 0.70Percentage of students who need help in both Mathematics and English = 55% = 0.55Part a)Since the percentages can also be expressed as probabilities,  we can say that:The probability that the selected person needs help in English and in Mathematics = P( E and M) = Percentage of students who need help in both Mathematics and English = 55%so,P(E and M) = 55% = 0.55Part b)The basic formula for probabilities of OR of two events is like:P(A or B) =P(A) + P(B) - P(A and B)Replacing A, B with E, M, we get:P(E or M)= P(E) + P(M) - P(E and M)Using the values, we get:P(E or M) = 0.80 + 0.70 - 0.55P(E or M) = 0.95 = 95%