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🎲 Chapter 7: The Mathematics of Maybe: Introduction to Probability • Exercise Set 7.3

Verified step-by-step solutions for your class notes.

Q1

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

Answer: The total number of possible outcomes (the sample size) is 6. The sample space is $\{1, 2, 3, 4, 5, 6\}$.

Q2

For the following experiments write down the sample space S.

  • (i) Rolling a die and tossing a coin together.
  • (ii) Choosing a random integer between -5 and +5.
  • (iii) A box containing 5 green and 7 red balls. One ball is drawn at random.
  • (i) $S = \{1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T\}$
  • (ii) Assuming inclusive: $S = \{ -4, -3, -2, -1, 0, 1, 2, 3, 4 \}$.
  • (iii) $S = \{\text{Green}, \text{Red}\}$.
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.'
  • (i) $S = \{\text{(Samosa, Chai)}, \text{(Samosa, Lassi)}, \text{(Pakora, Chai)}, \text{(Pakora, Lassi)}, \text{(Bhaji, Chai)}, \text{(Bhaji, Lassi)}\}$
  • (ii) Event $E = \{\text{(Samosa, Chai)}, \text{(Samosa, Lassi)}\}$