Question

In a class there are

Answer 1

Answer:

the probability that a student chosen at random plays football or cricket or both = $\frac{1}{5} + \frac{2}{5} + \frac{4}{15} = \frac{13}{15}$

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 = $\frac{6}{30} = \frac{1}{5}$

ix) the probability a student chosen at random plays cricket = $\frac{12}{30} = \frac{2}{5}$

x) the probability a student chosen at random plays both football and cricket = $\frac{8}{30} = \frac{4}{15}$

xi) therefore the probability that a student chosen at random plays football or cricket or both = $\frac{1}{5} + \frac{2}{5} + \frac{4}{15} = \frac{13}{15}$