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# work

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In a certain Algebra 2 class of 21 students, 6 of them play basketball and 14 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

May 2, 2023

#1
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The probability that a student is chosen randomly from the class plays both basketball and baseball is 4/21

Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

If the total number of people in the class is 21 students, hence the total outcome is 21

Get the number of students that plays both basketball and baseball

n(U) = n(B)only + n(Ba)only + n(BnBa) + n(BuBa)'

21 = 6-x + 14-x + x + 5

21 = 25 -x

x = 25 - 21

x = 4

Hence 4 students play both basketball and baseball

Hence the probability that a student chosen randomly from the class plays both basketball and baseball is 4/21

May 2, 2023
#2
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That seems good! Here is a shorter way: 21-5=16 who play either sport.

14+6=20 total sports. 20-16=4 players who play both sports. Therefore the probability is 4/21.

gb1falcon  May 3, 2023
#3
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Wow! Never knew I could do it like that! Thanks!

acyclics  May 3, 2023