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QuestionFind the probability that a randomly chosen student is male OR received a grade of "B" from the data:
Males: A=20, B=3, C=6; Females: A=17, B=9, C=12. Total=67. Round your answer to three decimal places.

Studdy Solution

STEP 1

Assumptions1. The total number of students is67. The number of male students is293. The number of students who received a grade of "B" is124. The event of being a male student and the event of receiving a grade of "B" are not mutually exclusive (i.e., there are male students who received a grade of "B")

STEP 2

First, we need to find the probability of a student being male. We can do this by dividing the number of male students by the total number of students.
(Male)=Number of male studentsTotal number of students(Male) = \frac{Number\, of\, male\, students}{Total\, number\, of\, students}

STEP 3

Now, plug in the given values for the number of male students and the total number of students to calculate the probability of a student being male.
(Male)=2967(Male) = \frac{29}{67}

STEP 4

Next, we need to find the probability of a student receiving a grade of "B". We can do this by dividing the number of students who received a grade of "B" by the total number of students.
(B)=Number of students who received a grade of "B"Total number of students(B) = \frac{Number\, of\, students\, who\, received\, a\, grade\, of\, "B"}{Total\, number\, of\, students}

STEP 5

Now, plug in the given values for the number of students who received a grade of "B" and the total number of students to calculate the probability of a student receiving a grade of "B".
(B)=1267(B) = \frac{12}{67}

STEP 6

To find the probability of a student being male OR receiving a grade of "B", we need to add the probabilities of these two events. However, as these events are not mutually exclusive, we have also counted the students who are male AND received a grade of "B" twice. Therefore, we need to subtract the probability of both events occurring.
(Male OR B)=(Male)+(B)−(Male AND B)(Male\, OR\, B) =(Male) +(B) -(Male\, AND\, B)

STEP 7

First, we need to find the probability of a student being male AND receiving a grade of "B". We can do this by dividing the number of male students who received a grade of "B" by the total number of students.
(Male AND B)=Number of male students who received a grade of "B"Total number of students(Male\, AND\, B) = \frac{Number\, of\, male\, students\, who\, received\, a\, grade\, of\, "B"}{Total\, number\, of\, students}

STEP 8

Now, plug in the given values for the number of male students who received a grade of "B" and the total number of students to calculate the probability of a student being male AND receiving a grade of "B".
(Male AND B)=367(Male\, AND\, B) = \frac{3}{67}

STEP 9

Now, plug in the calculated probabilities for(Male),(B), and(Male AND B) into the formula for(Male OR B) to find the probability of a student being male OR receiving a grade of "B".
(Male OR B)=2967+1267−367(Male\, OR\, B) = \frac{29}{67} + \frac{12}{67} - \frac{3}{67}

STEP 10

Calculate the probability of a student being male OR receiving a grade of "B".
(Male OR B)=2967+1267−367=3867(Male\, OR\, B) = \frac{29}{67} + \frac{12}{67} - \frac{3}{67} = \frac{38}{67}The probability that the student was male OR received a grade of "B" is 3867\frac{38}{67} or approximately0.567 when rounded to three decimal places.

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