Answer: 13/15
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Step-by-step explanation:
20 people play cricket, 8 of them play both, so 20-8 = 12 people play cricket only.
14 play football, 8 play both, so 14-8 = 6 play football only
We have,
- 12 people play cricket only
- 6 people play football only
- 8 people play both cricket and football
So far, this tallies to A = 12+6+8 = 26 people who play one sport only, or both sports mentioned. Now add in the four people who play neither sport and we get to B = 26+4 = 30 students overall.
The probability of selecting someone who plays at least one of the two sports mentioned is A/B = 26/30 = (13*2)/(15*2) = 13/15
This is effectively saying: if we had 15 students, then 13 of them play at least one of the two sports mentioned.