A group of 70 students were surveyed about the subjects they offer: English (E), Mathematics (M), and Geography (G). The following information was collected: 26 students offer all three subjects, 9 of

Step 7: Calculate n(M only). All students offer at least one subject, so the sum of all regions must equal the total number of students. n(E M G) = a + b + c + d + e + f + g = 70 Substitute the values found: a=6, c=4, d=9, e=12, f=8, g=26. 6 + b + 4 + 9 + 12 + 8 + 26 = 70 b + 65 = 70 b = 70 - 65 b = 5 So, n(M only) = 5. The number of students in each region of the Venn diagram is: • n(E only) = 6 • n(M only) = 5 • n(G only) = 4 • n(E M only) = 9 • n(E G only) = 12 • n(M G only) = 8 • n(E M G) = 26 a) Illustrate the information in a Venn diagram. A Venn diagram with three intersecting circles (E, M, G) would show the following values in their respective regions: • Region E only: 6 • Region M only: 5 • Region G only: 4 • Region E and M only (not G): 9 • Region E and G only (not M): 12 • Region M and G only (not E): 8 • Region E, M, and G (all three): 26 b) Determine the number of students who offer: i) mathematics The number of students who offer Mathematics is the sum of all regions within the Mathematics circle. n(M) = n(M only) + n(E M only) + n(M G only) + n(E M G) n(M) = b + d + f + g n(M) = 5 + 9 + 8 + 26 n(M) = 48 The number of students who offer mathematics is 48. ii) mathematics and economics but not geography This corresponds to the region where Economics and Mathematics circles overlap, but outside the Geography circle. This is represented by d. n(M E G^c) = d n(M E G^c) = 9 The number of students who offer mathematics and economics but not geography is 9. iii) The probability that a student selected at random from the class offer geography only. The number of students who offer Geography only is c = 4. The total number of students in the class is n(U) = 70. The probability is given by: P(Geography only) = Number of students who offer Geography onlyTotal number of students P(Geography only) = (c)/(n(U)) P(Geography only) = (4)/(70) Simplify the fraction: P(Geography only) = (2)/(35) The probability that a student selected at random from the class offers geography only is (2)/(35). Send me the next one 📸