Final answer:
The probability of winning at least one prize when buying a ticket each month for five months in a lottery with a single ticket win probability of 0.11 is approximately 0.4416.
Step-by-step explanation:
If you buy a ticket in the provincial lottery, then the probability that you will win a prize is 0.11.
Since the probability of winning is independent from month-to-month, if you buy one ticket each month for five months, the probability of not winning any prize in a single month is 1 - 0.11 = 0.89.
To find the probability that you will win at least one prize over the five months, you need to calculate the probability of not winning at all over the five months and then subtract this from 1.
The probability of not winning at all in five months is 0.89^5. So the probability of winning at least one prize in five months is 1 - 0.89^5.
Let's calculate this:
1 - 0.89^5 = 1 - (0.89 × 0.89 × 0.89 × 0.89 × 0.89) = 1 - 0.558405 = 0.441595
Therefore, the probability that you will win at least one prize if you buy one ticket each month for five months is approximately 0.4416 (rounded to four decimal places).