Out of 65players 11play basketball only,33play cricket only.if the num of cricket players is twice the num of basketball player.find the num of people who play both games and who don’t play any games.by using vena diagram

Cannot draw Venn diagram on these posts.

To solve this problem using a Venn diagram, follow these steps:

Step 1: Draw two overlapping circles to represent basketball and cricket players.

Step 2: Label one circle as "Basketball" and the other circle as "Cricket."

Step 3: Write the given information in the appropriate sections of the Venn diagram.

- According to the question, there are 65 players in total.
- It states that out of the 65 players, 11 play basketball only, and 33 play cricket only.

Place the number 11 in the Basketball circle (outside the overlap) and the number 33 in the Cricket circle (outside the overlap).

Step 4: Calculate the number of people who play both games and fill it in the overlapping region.

- The question states that the number of cricket players is twice the number of basketball players.
- Therefore, the number of basketball players is n, and the number of cricket players is 2n, where n is the number of people who play basketball.

Since 33 is twice 11 (33 = 2 x 11), n = 11.

So, the number of people who play both games is 11.

Fill in the overlapping region of the Venn diagram with the number 11.

Step 5: Calculate the number of people who don't play any games.

- To find the number of people who don't play any games, add up the numbers in the regions where no game is played.

In this case, we need to add the number of people who don't play basketball and don't play cricket.

To find the number of people who don't play basketball, subtract the number of people who play basketball only from the total number of players:

65 - 11 = 54.

Write 54 outside the Basketball circle.

To find the number of people who don't play cricket, subtract the number of people who play cricket only from the total number of players:

65 - 33 = 32.

Write 32 outside the Cricket circle.

Step 6: Analyze the Venn diagram to find the final results.

- The number in the overlapping region represents the number of people who play both games. In this case, it is 11.
- The number outside the circles represents the number of people who don't play any games. In this case, it is 54 (outside the Basketball circle) and 32 (outside the Cricket circle).

So, the number of people who play both games is 11, and the number of people who don't play any games is 54 + 32 = 86.

To solve this problem using a Venn diagram, follow these steps:

Step 1: Draw two overlapping circles to represent basketball and cricket.

Step 2: Label the intersection of the two circles as "Both."

Step 3: Write the given information in the appropriate sections of the circles.

- We know that 11 players play only basketball, so write "11" in the basketball circle but outside the intersection.
- We also know that 33 players play only cricket, so write "33" in the cricket circle but outside the intersection.
- It is given that the number of cricket players is twice the number of basketball players, so if "x" represents the number of basketball players, then "2x" represents the number of cricket players. Write these values inside the respective circles.

Step 4: Calculate the values for "x" and "2x" using the given information.
- From the problem statement, we have: "x + 11" (players who play basketball only) + "2x + 33" (players who play cricket only) = 65 (total number of players).
- Simplify the equation: 3x + 44 = 65.
- Solving for "x," we find that x = 7. Hence, there are 7 basketball players and 14 cricket players.

Step 5: Complete the Venn diagram based on the calculated values.
- In the basketball circle, write "11" (players who play only basketball) and "7" (players who play both).
- In the cricket circle, write "14" (players who play only cricket) and "7" (players who play both).

Step 6: Determine the number of people who don't play any games.
- Subtract the total number of players who play either basketball or cricket from the total number of players.
- In this case, it is 65 - (11 + 7 + 14) = 65 - 32 = 33.
- Therefore, there are 33 people who don't play any games.

So, based on the Venn diagram, the number of people who play both games is 7, and the number of people who don't play any games is 33.

If x play both, then

33+x = 2(11+x)
x = 11
65-(33+22-11) = 21 play neither