P(people have Syndrome X) = 0.02
P(positive result | have Syndrome X) = 0.9
P(positive result | don't have Syndrome X) = 0.1
P(positive result) = P(positive result | have Syndrome X) *
P(have Syndrome X) + P(positive result | don't have Syndrome X) *
P(don't have Syndrome X)
                         Â
= 0.9 * 0.02 + 0.1 * (1 - 0.02)
                         Â
= 0.116
P(have Syndrome X | positive result) = P(positive result | have
Syndrome X) * P(have Syndrome X) / P(positive result)
                                                         Â
= 0.9 * 0.02 / 0.116
                                                         Â
= 0.1552 ( ans)
