Prawdopodobieństwo zadanie

[kosin]

Ogromna prośba o pomoc w rozwiązaniu zadania, dla Was to pewnie będzie chwila a ja nie mam pomysłu ;(

The proportion of pregnant women amongst women that take a particular
pregnancy test is 75%. Two thirds of the pregnant women are at an early stage of
pregnancy. If a woman that takes the test is pregnant at an early stage the test will
be positive (indicate that she is pregnant) with probability 0.88. If she is pregnant
at a later stage it will be positive with probability 0.96. If she is not pregnant it will
be positive with probability 0.2.
(a) What is the probability the test will be positive?
(b) Given that a woman took the test and it was positive, what is the probability
that she is pregnant (at any stage)?
(c) Given that a woman took the test and it was negative, what is the probability
that she is pregnant (at any stage)?
(d) What is the probability the test will show a false result?

Pozdrawiam!