(III, IV) $(i)$ This is not an equally likely event because the outcome depends on the mechanical condition of the car. The probability of the car starting is not necessarily equal to the probability of it not starting.
$(ii)$ This is not an equally likely event because the outcome depends on the player's skill and practice,which are not uniform for every attempt.
$(iii)$ This is an equally likely event because there are only two possible outcomes (right or wrong),and assuming no prior knowledge,each has an equal chance of occurring.
$(iv)$ This is an equally likely event because the biological probability of a baby being a boy or a girl is considered to be $50\%$ each,assuming no other external factors.