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. let
m = the selected person needs in mathematics
e = the selected person needs in english
the probability that the selected person needs in english and in mathematics, i. e., p(e and m) is
the probability that the selected person needs in english or in mathematics, i. e., p(e or m) is

P(E and M) = 55% = 0.55

P(E or M) = 0.95 = 95%

Step-by-step explanation:

Percentage of students who need help in mathematics  = 80% = 0.80

Percentage of students who need help in English  = 70% = 0.70

Percentage of students who need help in both Mathematics and English = 55% = 0.55

Part 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% = 0.55

Part 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 - 0.55

P(E or M) = 0.95 = 95%

597

step-by-step explanation:

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step-by-step explanation: