Solving problem N4121 Bayesian probability theory

4121. Shooting at three types of targets, five of which are type A targets, three targets of type B and three targets of type C. The probability of hitting a target A is 0.4, a target of type B is 0.1, and a target C - 0.15. Find the probability that: a) the target will be hit at one shot, if it is not known what type of target it was made; b) with one shot (if it is not known what type of target it is made of) a target of type A will be hit.