A fair dice is thrown untill a score of less than 5 points is obtained. Find the probability of obtaining not less than 2 points on the last thrown

Options

A. (a)`3/4`
B. (b)`4/5`
C. (c)`5/6`
D. (d)`1/2`

Explanation

To solve the problem, we need to find the probability of obtaining not less than 2 points on the last throw of a fair die, given that we are throwing the die until we get a score of less than 5 points.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We are throwing a fair die repeatedly until we get a score of less than 5 points. The possible scores on a die are 1, 2, 3, 4, 5, and 6. The scores less than 5 are 1, 2, 3, and 4.

2. **Identifying the Last Throw Condition**:
We need to find the probability that the last score (the score that causes us to stop throwing) is not less than 2 points. This means the last score must be either 2, 3, or 4.

3. **Possible Outcomes on the Last Throw**:
The outcomes that lead to stopping the game (i.e., scores less than 5) are:
- 1 (stop)
- 2 (stop)
- 3 (stop)
- 4 (stop)

Therefore, the possible outcomes for the last throw are 1, 2, 3, and 4.

4. **Favorable Outcomes**:
The favorable outcomes for our condition (not less than 2 points) are:
- 2
- 3
- 4

Thus, there are 3 favorable outcomes (2, 3, and 4).

5. **Total Outcomes**:
The total outcomes that lead to stopping the game (the scores less than 5) are 1, 2, 3, and 4. Hence, there are 4 total outcomes.

6. **Calculating the Probability**:
The probability of obtaining not less than 2 points on the last throw is calculated as:
\[ P(\text{not less than 2 points}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{4} \]

7. **Final Answer**:
Therefore, the probability of obtaining not less than 2 points on the last throw is \(\frac{3}{4}\).