in a class there are
8 students who play football and cricket
4 students who do not play football or cricket
14 students who play football
20 students who play cricket
find the probability that a student chosen at random plays football or cricket or both

dont necessarily need an explanation but if you have a simple one i can understand then please do tell me x

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]

yoodyannapolis yoodyannapolis · Answer 2 · 2021-11-26T08:12:51+01:00

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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