Total number of boys = 200
Number of left handed boys = 50
If a students is known to be a boy, the probability that he is left handed will be equal to = (Number of left handed boys) / (Total Number of boys)
So, If a students is known to be a boy, the probability that he is left handed will be = [tex] \frac{50}{200} = \frac{1}{4} [/tex]
Thus, the correct answer is option B