Studdy AI Logo
Math

QuestionFind the numbers for athletes and musicians in a Venn diagram if P(A∣B)=715P(A|B) = \frac{7}{15}, with 25 athletes and 15 musicians admitted.

Studdy Solution

STEP 1

Assumptions1. Event A represents the athletes offered admission. Event B represents the musicians offered admission3. The total number of athletes offered admission is254. The total number of musicians offered admission is155. The probability that an athlete is offered admission, given that they were also involved in music, is 715\frac{7}{15}

STEP 2

First, we need to find the number of athletes who were also involved in music. This can be found by multiplying the total number of athletes offered admission by the given probability.
Number of athletes who are also musicians=Total number of athletestimesProbability of an athlete being a musicianNumber\, of\, athletes\, who\, are\, also\, musicians = Total\, number\, of\, athletes \\times Probability\, of\, an\, athlete\, being\, a\, musician

STEP 3

Now, plug in the given values for the total number of athletes and the probability to calculate the number of athletes who are also musicians.
Number of athletes who are also musicians=25times715Number\, of\, athletes\, who\, are\, also\, musicians =25 \\times \frac{7}{15}

STEP 4

Calculate the number of athletes who are also musicians.
Number of athletes who are also musicians=25times715=11.67Number\, of\, athletes\, who\, are\, also\, musicians =25 \\times \frac{7}{15} =11.67

STEP 5

Since we cannot have a fraction of a student, we round this number to the nearest whole number. So, there are12 athletes who are also musicians.

STEP 6

Now that we have the number of athletes who are also musicians, we can find the number of athletes who are not musicians. This can be found by subtracting the number of athletes who are also musicians from the total number of athletes.
Number of athletes who are not musicians=Total number of athletes−Number of athletes who are also musiciansNumber\, of\, athletes\, who\, are\, not\, musicians = Total\, number\, of\, athletes - Number\, of\, athletes\, who\, are\, also\, musicians

STEP 7

Plug in the values for the total number of athletes and the number of athletes who are also musicians to calculate the number of athletes who are not musicians.
Number of athletes who are not musicians=25−12Number\, of\, athletes\, who\, are\, not\, musicians =25 -12

STEP 8

Calculate the number of athletes who are not musicians.
Number of athletes who are not musicians=25−12=13Number\, of\, athletes\, who\, are\, not\, musicians =25 -12 =13

STEP 9

Similarly, we can find the number of musicians who are not athletes. This can be found by subtracting the number of athletes who are also musicians from the total number of musicians.
Number of musicians who are not athletes=Total number of musicians−Number of athletes who are also musiciansNumber\, of\, musicians\, who\, are\, not\, athletes = Total\, number\, of\, musicians - Number\, of\, athletes\, who\, are\, also\, musicians

STEP 10

Plug in the values for the total number of musicians and the number of athletes who are also musicians to calculate the number of musicians who are not athletes.
Number of musicians who are not athletes=15−12Number\, of\, musicians\, who\, are\, not\, athletes =15 -12

STEP 11

Calculate the number of musicians who are not athletes.
Number of musicians who are not athletes=15−=3Number\, of\, musicians\, who\, are\, not\, athletes =15 - =3So, the Venn diagram should be filled as follows-13 athletes who are not musicians- athletes who are also musicians-3 musicians who are not athletes

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord