Let six children ${\mathrm{B}}_1,{\mathrm{B}}_2,{\mathrm{B}}_3,{\mathrm{B}}_4,{\mathrm{B}}_5,{\mathrm{B}}_6$ each have a fair 6 sided die which they roll simultaneously. Let E denotes the event that atleast three of them roll a prime number and F denotes the event that  ${\mathrm{B}}_1,{\mathrm{B}}_2,{\mathrm{B}}_3$ throw a prime number. If the conditional probability of F given E is equal to $\frac{\mathrm{a}}{\mathrm{b}}$ where a and b are coprime then which is/are CORRECT ?