Respuesta :
Answer:
the probability that a student chosen at random plays football or cricket or both = [tex]\frac{1}{5} + \frac{2}{5} + \frac{4}{15} = \frac{13}{15}[/tex]
Step-by-step explanation:
i) 8 students play football and cricket
ii) 4 students do not play football or cricket
iii) total of 14 students play football.
iv) therefore the number of students who play only football is = 14 - 8 = 6
v) total of 20 students play cricket.
vi) therefore the number of students who play only cricket is = 20 - 8 = 12
vii) therefore the total number of students = 8 + 4 + 6 + 12 = 30
viii) the probability a student chosen at random plays football = [tex]\frac{6}{30} = \frac{1}{5}[/tex]
ix) the probability a student chosen at random plays cricket = [tex]\frac{12}{30} = \frac{2}{5}[/tex]
x) the probability a student chosen at random plays both football and cricket = [tex]\frac{8}{30} = \frac{4}{15}[/tex]
xi) therefore the probability that a student chosen at random plays football or cricket or both = [tex]\frac{1}{5} + \frac{2}{5} + \frac{4}{15} = \frac{13}{15}[/tex]
The probability that a student chosen at random plays football or cricket or both is [tex]\frac{13}{15}[/tex].
We have
Number of students play football and cricket = 8
Number of students do not play football or cricket = 4
Total Number of students play football = 14
Therefore, the number of students who play only football
= 14 - 8
= 6
Total Number of students play cricket = 20
Therefore, the number of students who play only cricket
= 20 - 8
= 12
So, the total number of students
= 8 + 4 + 6 + 12
= 30
Now, the probability that a student chosen at random plays football
[tex]=\frac{6}{30} \\=\frac{1}{5}[/tex]
The probability that a student chosen at random plays cricket
[tex]=\frac{12}{30} \\=\frac{2}{5}[/tex]
The probability a student chosen at random plays both football and cricket [tex]=\frac{8}{30} \\=\frac{4}{15}[/tex]
Therefore, the probability that a student chosen at random plays football or cricket or both
[tex]=\frac{1}{5} +\frac{2}{5}+\frac{4}{15}\\=\frac{3}{15} +\frac{6}{15}+\frac{4}{15}\\=\frac{13}{15}[/tex]
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