Question

Let’s suppose that 75% of planets have a north and that of the planets that have a north, 32% of them have two moons. On the other hand, 72% of planets that don’t have a north have two moons. What is the probability that a planet that does not have two moons has a north

Answer 1

P(planets have north) = 0.75

P(have two moons | planets have north) = 0.32

P(have two moons | planets don't have north) = 0.72

P(have two moons) = P(have two moons | planets have north) * P(planets have north) + P(have two moons | planets don't have north) * P(planets don't have north)

                                = 0.32 * 0.75 + 0.72 * (1 - 0.75)

                                = 0.42

P(don't have two moons) = 1 - P(have two moons) = 1 - 0.42 = 0.58

P(don't have two moons | planets have north) = 1 - P(have two moons | planets have north) = 1 - 0.32 = 0.68

P(planet has north | don't have two moons) = P(don't have two moons | planets have north) * P(planets have north) / P(don't have two moons)

                                                                      = 0.68 * 0.75 / 0.58

                                                                      = 0.8793 (ans)