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So, the best way to understand this question is by making a Venn diagram. From the information above, Total number (no.) students= 30 No. of students who don't play any sport= 4 No. of students who play only Football= 6 No. of students who play only cricket= 12 No. of students who play both the sports= 8 Probability of a student who plays football= (Total no. of students who play football)/ (Total number of students) =14/30 Probability of a student who plays cricket = (Total no. of students who play cricket)/ (Total no. of students) =20/30 =2/3 Probability of a student who plays both the sports= (Total number of students who play sports)/ (Total number of students) =26/30 =13/15
The best way to answer questions like these is with a Venn diagram. You will need to draw 2 circles that slightly overlap. The overlap is both football and cricket so we write 8 in this gap. The question tells us that 14 students play football but doesnt tell us that they only play football. This means that we must subtract 8 from 14 giving us 6. this goes in one circle. The same applies to 20 students that plays cricket so again we minus 8 from 20 giving us 12. This is written in the other circle. We are also told that 4 students do not play either so this is written outside the circles. Now we have our Venn diagram we can work out the probability. We need to find the total of students so we add all the numbers in the diagram together; 6+8+12+4 = 30 We also need to find the total amount that play cricket or football or both so 6+8+12 = 26 Therefore the answer is 26/30.
I would recommend drawing this out in a Venn diagram. Start with the middle section (8 students play both football and cricket). Then, you have 14 students in total that play football (14 - 8 = 6) and 20 students in total who play cricket (20 - 8 = 12). If you add all of the students who play football or cricket or both you get 26 (8 + 6 + 12 = 26). There are 4 students who do not play football or cricket, so 30 students in total (26 + 4 = 30). Therefore, the probability of choosing a student who plays football or cricket or both is 26/30.
Asked by Marlxn