To find the theoretical probability that it will rain less than 2 centimeters on day 11 based on the previous 10 days of rainfall data, we first need to determine how many of those 10 days had rainfall less than 2 centimeters.
Let's count the days with less than 2 centimeters of rain:
- Day 1: 1.2 cm (less than 2)
- Day 2: 2.0 cm (not less than 2)
- Day 3: 1.4 cm (less than 2)
- Day 4: 5.6 cm (not less than 2)
- Day 5: 1.8 cm (less than 2)
- Day 6: 0 cm (less than 2)
- Day 7: 0 cm (less than 2)
- Day 8: 3.4 cm (not less than 2)
- Day 9: 2.1 cm (not less than 2)
- Day 10: 1.9 cm (less than 2)
Now, let's count how many days had rainfall less than 2 centimeters:
- Day 1: 1.2 cm
- Day 3: 1.4 cm
- Day 5: 1.8 cm
- Day 6: 0 cm
- Day 7: 0 cm
- Day 10: 1.9 cm
That makes a total of 6 days.
Next, we calculate the probability that it will rain less than 2 centimeters on day 11:
\[ \text{Probability} = \frac{\text{Number of days with less than 2 cm}}{\text{Total number of days}} = \frac{6}{10} = 0.6 \]
Now, we convert this probability into a percentage:
\[ 0.6 \times 100 = 60% \]
Thus, the theoretical probability that it will rain less than 2 centimeters on day 11 is 60%.