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🎲 Chapter 7: The Mathematics of Maybe: Introduction to Probability • Exercise Set 7.4

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Exercise Set 7.1 1Exercise Set 7.2 4Exercise Set 7.3 3Exercise Set 7.4 1End-of-Chapter Exercises 8All Exercises 17
Q1

There are two fruit baskets A and B. Basket A has one apple and two oranges. Basket B has one banana and one mango. You randomly pick one fruit from each basket.

  • (i) Draw a tree diagram showing all possible pairs of fruits.
  • (ii) List the sample space.
  • (iii) What is the probability of picking one apple and one banana?
  • (i) Tree Diagram:
    From start, 2 branches for Basket A: Apple (prob 1/3) and Orange (prob 2/3).
    From Apple, 2 branches for Basket B: Banana (prob 1/2) and Mango (prob 1/2).
    From Orange, 2 branches for Basket B: Banana (prob 1/2) and Mango (prob 1/2).
  • (ii) Sample Space: $S = \{\text{(Apple, Banana)}, \text{(Apple, Mango)}, \text{(Orange, Banana)}, \text{(Orange, Mango)}\}$
  • (iii) Probability: P(Apple from A) $\times$ P(Banana from B) = $(1/3) \times (1/2) = \mathbf{1/6}$.
Basket A Basket B Outcome (Prob) 1/3 2/3 Apple Orange 1/2 1/2 Banana Mango 1/2 1/2 Banana Mango (A, B) → 1/6 (A, M) → 1/6 (O, B) → 2/6 = 1/3 (O, M) → 2/6 = 1/3
Tree Diagram of picking one fruit from Basket A and one from Basket B