To find the probability that a pupil chosen at random is at least 11 years old, we need to consider the number of pupils aged 11 and older (which includes those who are 11 and 12) and divide it by the total number of pupils.

Number of pupils aged 11 and older = Number of 11-year-olds + Number of 12-year-olds = 27 + 7 = 34

Total number of pupils = Sum of all pupils in the age groups = 6 + 27 + 7 = 40

Now, let's calculate the probability:

Probability = Number of pupils aged 11 and older / Total number of pupils = 34 / 40

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

Probability = (34 ÷ 2) / (40 ÷ 2) = 17 / 20

So, the correct answer is option B: 17/20.0