A school offers drumming and trumpet lessons to a group of 50 students.of these children, 24attend drumming lessons,19 attend trumpet lessons and 13 attend neither drumming nor trumpet lessons.1)illustrate the information in a venn diagram.2)what is the probability of meeting who attend only drumming lessons.

Now, draw two overlapping circles within the rectangle. Label one set 'D' to represent children who attended drumming lessons and label the second set 'T' to represent children attending trumpet lessons. The overlapping region indicates the intersection of the two sets, representing the number of children who attend both drumming and trumpet lessons.

Since 13 students attend neither drumming nor trumpet lessons, write the number 13 in the area outside the circles but within the rectangle.

Given that 24 students attend drumming lessons and 19 attend trumpet lessons, with 13 attending neither drumming nor trumpet lessons, the total is calculated as follows:

24 + 19 + 13 = 56

Since the total number of students is 50, it indicates some students are counted twice. To determine the number of students attending both drumming and trumpet lessons, subtract the total (50) from the sum (56):

Drumming and trumpet lessons = 56 - 50 = 6

Therefore, we place the number 6 in the region where the circles overlap.

To find the remaining numbers to fill in the circles, subtract the number in the overlapping region from the total number of each set.

So, to find the number of students who attend drumming lessons only, subtract the number attending both lessons (6) from the total attending drumming lessons (24):

Drumming lessons only = 24 - 6 = 18

Therefore, place the number 18 in the region of circle D that does not overlap circle T.

Similarly, to find the number of students who attend trumpet lessons only, subtract the number attending both lessons (6) from the total attending trumpet lessons (19):

Trumpet lessons only = 19 - 6 = 13

Therefore, place the number 13 in the region of circle T that does not overlap circle D.

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Question 2

To find the probability of meeting a student who attends only drumming lessons, we need to divide the number of students who attend only drumming lessons by the total number of students.

We have already determined that 18 students attend only drumming lessons, and the total number of students is 50. So, the probability of meeting a student who attends only drumming lessons is:

[tex]\text{Probability} = \dfrac{\text{Number of students attending only drumming lessons}}{\text{Total number of students}}\\\\\\\text{Probability} = \dfrac{18}{50} \\\\\\\text{Probability} = 0.36[/tex]

Therefore, the probability of meeting someone who attends only drumming lessons is 0.36 or 36%.