To solve the problem step by step, let's first summarize the contents of the bag and the possible outcomes when drawing balls.
### Step 1: Identify the contents of the bag
The bag contains:
- 3 red balls with numbers 1, 2, and 3
- 2 black balls with numbers 4 and 6
Thus, the balls can be represented as:
- R1 (1), R2 (2), R3 (3), B4 (4), B6 (6)
### Step 2: Determine the total number of outcomes
Since a ball is drawn, its number is noted, and then it is replaced before drawing again, the total number of outcomes can be calculated as follows:
- Total balls = 5 (3 red + 2 black)
- Total outcomes when drawing two balls = 5 (first draw) × 5 (second draw) = 25 outcomes
### Step 3: Solve each part of the question
#### Part (i): Probability of drawing 2 on the first draw and 6 on the second draw
- The specific outcome we are looking for is (2, 6).
- There is only **1** favorable outcome: (2, 6).
**Probability** = Number of favorable outcomes / Total outcomes = 1 / 25
#### Part (ii): Probability of drawing a number ≤ 2 on the first draw and 4 on the second draw
- The possible outcomes for the first draw (number ≤ 2) are 1 and 2.
- The second draw is fixed at 4.
- The favorable outcomes are:
- (1, 4)
- (2, 4)
Thus, there are **2** favorable outcomes.
**Probability** = Number of favorable outcomes / Total outcomes = 2 / 25
#### Part (iii): Probability of drawing a total of 5
- We need to find pairs of outcomes that sum to 5:
- (1, 4)
- (2, 3)
Thus, there are **2** favorable outcomes.
**Probability** = Number of favorable outcomes / Total outcomes = 2 / 25
### Final Answers:
- (i) Probability of drawing 2 on the first draw and 6 on the second draw: **1/25**
- (ii) Probability of drawing a number ≤ 2 on the first draw and 4 on the second draw: **2/25**
- (iii) Probability of drawing a total of 5: **2/25**
