Question 2

We will list all possible outcomes and then use them to find the required probability.

Step 1 — List all outcomes

First, let's identify the colours of pens available. We have Red (R), Black (B), and Green (G) pens. You pick a pen and put it back. Your friend then picks a pen. The possible outcomes for your pick are R, B, or G. The possible outcomes for your friend's pick are also R, B, or G. We can list all combinations as ordered pairs. The first letter is your pick, and the second is your friend's pick. The set of all possible outcomes is called the sample space. $S = \{(R, R), (R, B), (R, G), (B, R), (B, B), (B, G), (G, R), (G, B), (G, G)\}$ The total number of possible outcomes is 9.

Step 2 — Find probability of same colour

We want to find the probability that both pick pens of the same colour. Let's look at our list of possible outcomes. We need to find outcomes where both letters are the same. These outcomes are (R, R), (B, B), and (G, G). The number of favourable outcomes is 3. The total number of possible outcomes is 9. We can calculate the probability. $P(\text{same colour}) = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$ $P(\text{same colour}) = \frac{3}{9}$ $P(\text{same colour}) = \frac{1}{3}$

$\boxed{\text{Probability} = \frac{1}{3}}$

Answer

(i) The possible outcomes of the pen colours are (R, R), (R, B), (R, G), (B, R), (B, B), (B, G), (G, R), (G, B), (G, G). (ii) The probability that both you and your friend pick pens of the same colour is $\frac{1}{3}$.