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In a group of 75 student 20 liked football only 30 liked cricket only and 18 did not like any of two game? i) How many of them liked at least on game? ii) find the number of student who liked both game. iii)how many of them liked cricket. iv) how many of them liked football. v) represent the result in venn diagram

Sagot :

Answers:

  • i) 57
  • ii) 7
  • iii) 37
  • iv) 27
  • v) See the venn diagram below

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Explanation:

We have these given facts

  • A. There are 75 students total.
  • B. There are 20 students who like football only
  • C. There are 30 students who like cricket only
  • D. There are 18 students who don't like either sport

Fact D indicates that 18 goes on the outside of the two circles, but inside the universal set shown by the rectangle.

We'll use facts A and D to find that 75-18 = 57 students like either football, cricket, or both. So the numbers inside the regions in the circles must add up to 57.

Now use the values from facts B and C. They add to 20+30 = 50. This is the number of students who either like football only OR like cricket only. None of these 50 students like both sports. But we found that 57 like one or the other or both. So that must mean 57-50 = 7 students like both sports.

We have enough info to fill out the venn diagram as shown below.

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Now to answer the questions your teacher asked:

  • i) How many of them liked at least on game? This would be the 57 value mentioned earlier.
  • ii) Find the number of student who liked both game. It's the value 7 found in the middle of the two circles.
  • iii)how many of them liked cricket. Add up the numbers in the "Cricket" circle to get 7+30 = 37.
  • iv) how many of them liked football. Add up the numbers in the "Football" circle to get 20+7 = 27
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