Math

QuestionFind the probability that a randomly selected student is taking a math or English class, given 68%68\% in math, 75%75\% in English, and 60%60\% in both. Round your answer to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The percentage of students taking a math class is68% . The percentage of students taking an English class is75%
3. The percentage of students taking both classes is60%
4. We are asked to find the probability that a randomly selected student is taking either a math class or an English class

STEP 2

We will use the formula for the probability of the union of two events, which is given by(AB)=(A)+(B)(AB)(A \cup B) =(A) +(B) -(A \cap B)where- (AB)(A \cup B) is the probability of event A (student taking a math class) or event B (student taking an English class) - (A)(A) is the probability of event A (student taking a math class) - (B)(B) is the probability of event B (student taking an English class) - (AB)(A \cap B) is the probability of both events A and B occurring (student taking both classes)

STEP 3

Now, plug in the given values for the probabilities of the events. Note that the percentages need to be converted to decimal form.
(AB)=0.68+0.750.60(A \cup B) =0.68 +0.75 -0.60

STEP 4

Calculate the probability.
(AB)=0.68+0.750.60=0.83(A \cup B) =0.68 +0.75 -0.60 =0.83The probability that a randomly selected student is taking a math class or an English class is0.83 or83% when expressed as a percentage.

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