Canteen and Coop Purchase Preferences A school interviewed 180 students to learn about their daily buying habits. Out of all respondents, 100 students said they usually buy food from the school canteen, 80 students buy items from the school cooperative shop, and 40 students shop at both places. Let: ⚫T = Set of students who buy from the canteen ⚫P = Set of students who buy from the cooperative a) Present the information above into Venn diagram. (3 marks) b)What is the probability that a randomly selected student does not buy from the cooperative shop? (2 marks) c) What is the probability that a randomly selected student buys from both the canteen and cooperative? (2 marks) d) Find P(T' U P)? Draw and shade the Venn Diagram to represent this event. (3 marks)
Answer (3)
− 9.5 × 1 0 − 3 = − 9.5 × 0.001 = − 0.0095
The number − 9.5 × 1 0 − 3 can be expressed in standard form as − 0.0095 by multiplying − 9.5 by 0.001 . This illustrates the power of ten notation to represent small numbers efficiently. Understanding how to convert scientific notation into decimal form is important in mathematics.
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Jawaban:*Problem:*Canteen and Coop Purchase Preferences*Given:*- Total students = 180- Students who buy from canteen (T) = 100- Students who buy from cooperative (P) = 80- Students who buy from both (T ∩ P) = 40*a) Venn Diagram:*Let's represent the information in a Venn diagram.- T (canteen) = 100- P (cooperative) = 80- T ∩ P (both) = 40- T only = 100 - 40 = 60- P only = 80 - 40 = 40- Neither T nor P = 180 - (60 + 40 + 40) = 40*Venn Diagram:*Two overlapping circles, one labeled T (canteen) and the other P (cooperative).- T circle: 60 (T only) and 40 (T ∩ P)- P circle: 40 (P only) and 40 (T ∩ P)- Outside both circles: 40 (neither T nor P)*b) Probability that a randomly selected student does not buy from the cooperative shop:*P(P') = (Number of students who do not buy from P) / Total students= (60 + 40) / 180= 100 / 180= 5/9*c) Probability that a randomly selected student buys from both the canteen and cooperative:*P(T ∩ P) = (Number of students who buy from both) / Total students= 40 / 180= 2/9*d) Find P(T' U P):*T' = Students who do not buy from canteen = 80P = Students who buy from cooperative = 80T' ∩ P = Students who do not buy from canteen but buy from cooperative = 40T' U P = Students who do not buy from canteen or buy from cooperative = 40 + 40 + 40 = 120P(T' U P) = 120 / 180= 2/3*Venn Diagram for T' U P:*Shade the area outside T (canteen) circle and the entire P (cooperative) circle.The shaded area includes:- P only (40)- T ∩ P (40)- Neither T nor P is not included in T' but P is included in the union, so the 40 students who are in P only and both are included in the union with the 40 students who are not in T but in P.The final answer for b) is $\boxed{\frac{5}{9}}$.The final answer for c) is $\boxed{\frac{2}{9}}$.The final answer for d) is $\boxed{\frac{2}{3}}$.
