examday

/TMUA

A child is chosen at random from a group. Each child is equally likely to be chosen.

Which of the following conditions is/are necessary for the probability that the child has a pet to equal exactly $4/9$?

I Exactly $5$ children in the group do not have a pet.

II The number of children in the group is divisible by $4$.

III The number of children in the group with a pet is divisible by $3$.