The Mathematics of Maybe: Introduction to Probability | Exercise 7.3

Question 3

In a village fair, there are 3 popular snacks available: Samosa, Pakora, and Bhaji. For drinks, villagers can choose either Chai or Lassi.

(i) List the sample space of all possible snack and drink combinations a person could choose at the fair.

(ii) List the event 'Selecting Samosa as a snack.'

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Solution
Understand the Question
  • There are 33 snacks (Samosa, Pakora, Bhaji) and 22 drinks (Chai, Lassi).
  • Each snack can be paired with either drink, giving a total of 3×2=63 \times 2 = 6 possible combinations in the sample space (SS).
  • An event is a subset of the sample space satisfying a specific condition (e.g., choosing Samosa as the snack).

(i) List the sample space of all possible snack and drink combinations a person could choose at the fair.

Step 1 · List all combinations in the sample space

Combine each of the 33 snacks with each of the 22 drinks:Diagram 1

S={(Samosa, Chai),(Samosa, Lassi),(Pakora, Chai),(Pakora, Lassi),(Bhaji, Chai),(Bhaji, Lassi)}S = \{(\text{Samosa, Chai}), (\text{Samosa, Lassi}), (\text{Pakora, Chai}), (\text{Pakora, Lassi}), (\text{Bhaji, Chai}), (\text{Bhaji, Lassi})\}

Total number of outcomes: n(S)=6n(S) = 6

Answer

(i) S={(Samosa, Chai),(Samosa, Lassi),(Pakora, Chai),(Pakora, Lassi),(Bhaji, Chai),(Bhaji, Lassi)}S = \{(\text{Samosa, Chai}), (\text{Samosa, Lassi}), (\text{Pakora, Chai}), (\text{Pakora, Lassi}), (\text{Bhaji, Chai}), (\text{Bhaji, Lassi})\}

(ii) List the event 'Selecting Samosa as a snack.'

Step 1 · Identify favorable outcomes and calculate probability

The event EE of selecting Samosa contains all pairs where Samosa is the snack:

E={(Samosa, Chai),(Samosa, Lassi)}E = \{(\text{Samosa, Chai}), (\text{Samosa, Lassi})\}

Number of favorable outcomes n(E)=2n(E) = 2.

P(Samosa)=Number of outcomes in ETotal number of outcomes in S=26=13\begin{aligned} P(\text{Samosa}) &= \dfrac{\text{Number of outcomes in } E}{\text{Total number of outcomes in } S} \\[0.6em] &= \dfrac{2}{6} \\[0.6em] &= \dfrac{1}{3} \end{aligned}
Answer

(ii) E={(Samosa, Chai),(Samosa, Lassi)}E = \{(\text{Samosa, Chai}), (\text{Samosa, Lassi})\}

Common Mistakes
  • Listing items individually: Writing individual items like {Samosa,Chai}\{\text{Samosa}, \text{Chai}\} instead of paired outcomes (Samosa, Chai)(\text{Samosa, Chai}).
  • Incomplete pairings: Forgetting to pair each snack with every drink option, leading to fewer than 3×2=63 \times 2 = 6 total outcomes.
  • Unsimplified probability: Leaving the probability as 26\dfrac{2}{6} instead of simplifying to lowest terms 13\dfrac{1}{3}.

More questions in Exercise 7.3

Q1

When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?

Q2

For the following experiments write down the sample space SS.

(i) Rolling a die and tossing a coin together.

(ii) Choosing a random integer between −5-5 and +5+5.

(iii) A box containing 5 green and 7 red balls. One ball is drawn at random.

Q3

In a village fair, there are 3 popular snacks available: Samosa, Pakora, and Bhaji. For drinks, villagers can choose either Chai or Lassi.

(i) List the sample space of all possible snack and drink combinations a person could choose at the fair.

(ii) List the event 'Selecting Samosa as a snack.'

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