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 45% of people have type O blood and 15% of people have Rh− factor; 49% of people have type O or Rh− factor.
Find the probability that a person has both type O blood and the Rh− factor.
P(O) = 0.45 P(R) = 0.15 \(P(O\cup R)=0.49\) The formula for the probability of one event or another can be written as: \(P(O\cup R)=P(O)+P(R)-P(O\cap R)\) Plugging in the given values, we get: \(0.49=0.45+0.15-P(O\cap R)\) which can be rearranged to find the probability that a person has both type O blood and the Rh− factor, as follows: \(P(O\cap R)=0.60-0.49=0.11\) So the required probability is 0.11 or as a percentage 11%.
