Respuesta :
Solution:
we are given that
In a certain algebra 2 class of 29 students, 22 of them play basketball and 12 of them play baseball.
There are 9 students who play both sports.
what is the probability that a student chosen randomly from the class plays basketball or baseball?
1 student out of 29 can be chosen in [tex] {29}_C_1 [/tex]ways.
1 student out of 22 Basketball player can be chosen in [tex] {22}_C_1 [/tex]ways.
1 student out of 12 baseball player can be chosen in [tex] {12}_C_1 [/tex]ways.
1 student out of 9 player can be chosen in [tex] {9}_C_1 [/tex]ways.
So Required Probability[tex] =\frac{22_C_1}{29_C_1}+ \frac{12_C_1}{29_C_1}-\frac{9_C_1}{29_C_1}=0.862\\ [/tex]
The probability helps us to know the chances of an event occurring. The probability that a student is chosen randomly from the class plays basketball or baseball is 0.862.
What is Probability?
The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given in the problem that the number of students who play basketball is 22, while the number of students who play baseball is 12. Also, it is mentioned that the number of students who play both the games is 9. Therefore, the possible number of ways that a student who either plays basketball or baseball can be selected is:
[tex]\text{Number of ways} = ^{22}C_1 + ^{12}C_1 - ^{9}C_1 = 22 + 12 - 9 =25[/tex]
Now, the total number of ways any student can be selected can be written as,
[tex]\text{Total number of ways} = ^{29}C_1 = 29[/tex]
Thus, the probability that a student chosen randomly from the class plays basketball or baseball is
[tex]\rm Probability = \dfrac{\text{Number of ways}}{\text{Total number of ways}} = \dfrac{25}{29} = 0.862[/tex]
Hence, the probability that a student chosen randomly from the class plays basketball or baseball is 0.862.
Learn more about Probability:
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