Question

Over the last ten days the average rainfall each day, in centimeters, is shown in the table.

day 1 : 1.2
day 2 : 2.0
day 3: 1.4
day 4: 5.6
day 5: 1.8
day 6: 0
day 7: 0
day 8: 3.4
day 9: 2.1
day 10: 1.9

The theoretical probability that it will rain less than 2 centimeters on day 11 is __%

Answer 1

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:

1. Day 1: 1.2 cm
2. Day 3: 1.4 cm
3. Day 5: 1.8 cm
4. Day 6: 0 cm
5. Day 7: 0 cm
6. 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%**.