Question

1. Unit 1: समूह (Sets) For Q.No. 1 in Final Examination UB) एउटा समुदायका 500 जना मानिसमा गरिएको सर्वेक्षणमा 250 जनाले फुटबल र 300 जनाले क्रिकेट मन पराए तर 25 जनाले कुनै पि खेल मन पराएनन् । यसको आधारमा तल सोधिएका प्रश्नहरूको उत्तर दिनुहोस् । In a survey of a community of 500 people, 250 like football, 300 liked cricket and 25 did not like any of the games. Answer the following questions. (a) माथिको तथ्यलाई भेनचित्रमा देखाउनुहोस् र दुवै खेल मन पराउने मानिसको सङ्ख्या पत्ता लगाउनुहोस् । Draw a Venn diagram to show the above facts and find the number of people who liked both games. (b) एउटा मात्र खेल मन पराउने मानिसको सङ्ख्या पत्ता लगाउनुहोस् । Find the number of people who liked only one game. (c) बढीमा एउटा खेल मन पराउने मानिसको सङ्ख्या पत्ता लगाउनुहोस् । Find the number of people who liked at most one game. (d) कम्तीमा एक खेल मन पराउने मानिसको सङ्ख्या पत्ता लगाउनुहोस् । Find the number of people who liked at least one game. CAUB [3] [Ans: 75 [1] [Ans: 400] [1] [Ans: 425 [1] [Ans : 47
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Answer 1

Answer:

$\text{1.}\\ \text{Let F denote the people who like football and C be the people who like }\\\text{cricket.}\\\text{Given, }\\\text{n(U) = 500}\\\text{n(F) = 250}\\\text{n(C) = 300}\\\text{n}(\overline{\text{F}\cup\text{C}})=25\\\text{n(F}\cap\text{C)}=x\text{ (Let)}$

$\text{a. Solution: }\\\\\text{(See the posted image for venn-diagram.)}\\\\\text{n(F}\cup\text{C)}=\text{n(U) }-\text{n}(\overline{\text{F}\cup\text{C}})\\\text{or, }250-x+x+300-x=500-25\\\text{or, }550-x=475\\\text{or, }x=550-475\\\text{or, }x=75$

$\text{b. }\\\text{Number of people who liked football only, n}_\circ(\text{F})=\text{n(F) }-\text{n}(\text{F}\cap\text{C})=250-75\\\therefore\ \text{n}_\circ(\text{F})=175\\\text{Number of people who liked cricket only, n}_\circ(\text{C})=\text{n(C) }-\text{n}(\text{F}\cap\text{C})=300-75\\\therefore\ \text{n}_\circ(\text{C})=225\\\text{So, number of people who liked only one game = }\text{n}_\circ(\text{C})+\text{n}_\circ(\text{F})=175+225\\\text{}\hspace{7.3cm}\text{= }400$

$\text{c. }\\\text{Number of people who liked at most one game = n}_\circ(\text{F})+\text{n}_\circ(\text{C})+\text{n}(\overline{\text{F}\cup\text{C}})\\\text{}\hspace{7.3cm}\text{= }175+225+25=425$

$\text{d.}\\\text{Number of people who liked at least one game = }\text{n(}\text{A}\cup\text{B})=250-x+x+300-x\\\text{}\hspace{9cm}\text{= }550-75=475$