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Statistical probability · 3 marks

Suppose you anonymously collect information regarding the favourite fruit of 50 students in your class. Let us assume that the results are: 20 students like mango, 15 students like apples, 10 students like bananas, and 5 students like grapes. Let us play a game! Suppose we randomly pick one student from the class and try to guess their favourite fruit. What’s the probability that the student’s favourite fruit is mango?

Answer: P(mango) = 2050 = 0.4, a 40% chance. Used for a school of 1500 students, this estimate means buying about 600 mangoes (40% of 1500).

Step-by-step solution

Given: 50 students: mango 20, apples 15, bananas 10, grapes 5
To find: The probability that a randomly chosen student’s favourite fruit is mango

Idea: Statistical probability is based on collected data: P = Number of students who like mangoTotal number of students. The same fraction can then estimate numbers in a bigger group.

  1. Check the total: 20 + 15 + 10 + 5 = 50 students.½ mark
  2. Probability of mango as the favourite fruit = Number of students who like mangoTotal number of students = 2050½ mark
  3. = 0.4. So there is a 0.4 or 40% chance that a randomly chosen student in the class likes mango.1 mark
  4. Using the estimate for the whole school. To buy fruit for a school of 1500 students, treat the class as a sample. Mangoes needed ≈ 0.4 × 1500 = 600 (40% of 1500); the remaining 900 would be other fruits (apples, bananas, grapes).1 mark
  5. A larger, more representative sample (for example 100 students from different classes) would make the estimate more reliable. Choosing such a sample is called sampling.
P(favourite fruit is mango) = 20/50 = 0.4, a 40% chance. For a school of 1500 students this estimates about 600 mangoes.

Check: The four probabilities 0.4 (mango), 0.3 (apples), 0.2 (bananas), 0.1 (grapes) add up to 1 ✓. For 1500 students they give 600 + 450 + 300 + 150 = 1500 ✓.

Answer to write in the exam

Total students = 20 + 15 + 10 + 5 = 50

P(mango) = Number of students who like mangoTotal number of students = 2050

= 0.4, i.e. 40%

For 1500 students: mangoes ≈ 0.4 × 1500 = 600

∴ P(favourite fruit is mango) = 0.4 (40%); about 600 mangoes for 1500 students

Common mistakes that cost marks

  • Dividing by the number of fruit types (4) instead of the number of students (50).
  • Writing 2030, comparing mango-lovers with the others instead of with the whole class.
  • For the school, multiplying 20 by 1500, or dividing 1500 by 20. Multiply the probability (0.4) by the total (1500).

How this can come in the exam

Case-based (4 marks)

A canteen manager asks a random sample of 60 students which snack they prefer: 27 choose samosa, 18 choose sandwich, 9 choose idli and 6 choose fruit chaat. The school has 1200 students.
(a) Find the probability that a student from the sample prefers samosa. (1)
(b) Find the probability that a student from the sample prefers idli or fruit chaat. (1)
(c) Estimate how many students in the school prefer sandwich. (2)

Show answer(a) 2760 = 0.45.
(b) (9 + 6)/60 = 1560 = 0.25.
(c) P(sandwich) = 1860 = 0.3; estimate = 0.3 × 1200 = 360 students.
MCQ (1 mark)

In a survey of 40 students, 14 said their favourite colour is blue. The probability that a randomly chosen student from the survey likes blue best is

  1. 0.14
  2. 0.35
  3. 0.4
  4. 1426
Show answer

(B) 0.35
1440 = 0.35.

Try one yourself

In a sample of 25 students, 8 walk to school. Estimate how many of the 750 students in the school walk to school.

Show answer

P(walks) = 825 = 0.32. Estimate = 0.32 × 750 = 240 students.

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