NCERT Solutions for Class 9 Maths Chapter 7 — Exercise Set 7.3#
The sample space $S$ lists every possible outcome exactly once; its number of elements $n(S)$ is the sample size. An event is a subset of the sample space.
1. When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space? #
Solution
$$S = \{1, 2, 3, 4, 5, 6\}$$
∴ There are 6 possible outcomes: $n(S) = 6$.
2. For the following experiments write down the sample space S. #
(i) Rolling a die and tossing a coin together.
Each of the 6 die faces can go with heads (H) or tails (T):
$$S = \{1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T\}$$$n(S) = 6 \times 2 = 12$.
(ii) Choosing a random integer between – 5 and + 5.
Taking the end points as included:
$$S = \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5\}$$$n(S) = 11$. (If “between” is taken to exclude $-5$ and $5$, then $S = \{-4, -3, \ldots, 3, 4\}$ with 9 elements.)
(iii) A box containing 5 green and 7 red balls. One ball is drawn at random.
If we record only the colour:
$$S = \{\text{Green}, \text{Red}\}$$These two outcomes are not equally likely. To get equally likely outcomes, label each ball:
$$S = \{G_1, G_2, G_3, G_4, G_5, R_1, R_2, R_3, R_4, R_5, R_6, R_7\}$$with $n(S) = 12$.
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.
Each of the 3 snacks can go with either of the 2 drinks:
| Snack | With Chai | With Lassi |
|---|---|---|
| Samosa | (Samosa, Chai) | (Samosa, Lassi) |
| Pakora | (Pakora, Chai) | (Pakora, Lassi) |
| Bhaji | (Bhaji, Chai) | (Bhaji, Lassi) |
$n(S) = 3 \times 2 = 6$.
(ii) List the event ‘Selecting Samosa as a snack.’
$$E = \{(\text{Samosa, Chai}), (\text{Samosa, Lassi})\}$$