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QuestionA group of students has grades summarized as follows: Males: A=18, B=7, C=14; Females: A=17, B=4, C=5. Find the probability a randomly chosen student did NOT get a "B", rounded to three decimal places.

Studdy Solution

STEP 1

Assumptions1. The total number of students is65. . The number of students who got a "B" is11.
3. The student is chosen at random, so each student has an equal chance of being chosen.

STEP 2

First, we need to find the number of students who did NOT get a "B". We can do this by subtracting the number of students who got a "B" from the total number of students.
Number of students who did NOT get a "B"=Total number of students−Number of students who got a "B"Number\, of\, students\, who\, did\, NOT\, get\, a\, "B" = Total\, number\, of\, students - Number\, of\, students\, who\, got\, a\, "B"

STEP 3

Now, plug in the given values for the total number of students and the number of students who got a "B" to calculate the number of students who did NOT get a "B".
Number of students who did NOT get a "B"=65−11Number\, of\, students\, who\, did\, NOT\, get\, a\, "B" =65 -11

STEP 4

Calculate the number of students who did NOT get a "B".
Number of students who did NOT get a "B"=65−11=54Number\, of\, students\, who\, did\, NOT\, get\, a\, "B" =65 -11 =54

STEP 5

Now that we have the number of students who did NOT get a "B", we can find the probability that a student chosen at random did NOT get a "B". This is the ratio of the number of students who did NOT get a "B" to the total number of students.
Probability that a student did NOT get a "B"=Number of students who did NOT get a "B"/Total number of studentsProbability\, that\, a\, student\, did\, NOT\, get\, a\, "B" = Number\, of\, students\, who\, did\, NOT\, get\, a\, "B" / Total\, number\, of\, students

STEP 6

Plug in the values for the number of students who did NOT get a "B" and the total number of students to calculate the probability.
Probability that a student did NOT get a "B"=54/65Probability\, that\, a\, student\, did\, NOT\, get\, a\, "B" =54 /65

STEP 7

Calculate the probability that a student chosen at random did NOT get a "B".
Probability that a student did NOT get a "B"=54/65≈0.831Probability\, that\, a\, student\, did\, NOT\, get\, a\, "B" =54 /65 \approx0.831The probability that a student chosen at random did NOT get a "B" is approximately0.831 or831/1000 when rounded to three decimal places.

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