Question 3

We will list all possible choices a person can make.

Step 1 — List all combinations

Let's list all snack and drink options. There are 3 snacks and 2 drinks. We combine each snack with each drink. This gives us all possible outcomes.

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

The total number of outcomes is 6.

$\boxed{n(S) = 6}$

Step 2 — Identify the event and its probability

We want the event 'Selecting Samosa as a snack'. Let's find outcomes where Samosa is chosen. These outcomes are (Samosa, Chai) and (Samosa, Lassi). There are 2 such outcomes.

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

The number of outcomes in event E is 2. The probability is the number of favorable outcomes divided by total outcomes.

$P(\text{Samosa}) = \frac{\text{Number of outcomes in E}}{\text{Total number of outcomes}}$

$P(\text{Samosa}) = \frac{2}{6}$

$P(\text{Samosa}) = \frac{1}{3}$

$\boxed{P(\text{Samosa}) = \frac{1}{3}}$

Answer

(i) The sample space is $S = \{(\text{Samosa, Chai}), (\text{Samosa, Lassi}), (\text{Pakora, Chai}), (\text{Pakora, Lassi}), (\text{Bhaji, Chai}), (\text{Bhaji, Lassi})\}$. The total number of outcomes is $n(S) = 6$. (ii) The event 'Selecting Samosa as a snack' is $E = \{(\text{Samosa, Chai}), (\text{Samosa, Lassi})\}$. The probability of this event is $P(\text{Samosa}) = \frac{1}{3}$.