A blood bank asserts that a person with type O blood and a negative Rh factor (Rh−) can donate blood to any person with any blood type. Their data show that 49% of people have type O blood and 15% of people have Rh− factor; 45% of people have type O or Rh− factor. Find the probability that a person has both type O blood and the Rh− factor.

Question

anonymous · Answer

$$P(O \cup Rh-) = 0.45$$
Additive Law of Probability
$$P(A \cup B) = P(A) + P(B) - P(AB)$$

Therefore,
$$P(O and Rh-) = P(O) + P(Rh-) - P(O \cup Rh-) = 0.49 + 0.15 - 0.45 = 0.19$$