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 41% of people have type O blood and 15% of people have Rh− factor; 47% of people have type O or Rh− factor.Part (a)Find the probability that a person has both type O blood and the Rh− factor.Part (b)Find the probability that a person does NOT have both type O blood and the Rh− factor.
Question
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 41% of people have type O blood and 15% of people have Rh− factor; 47% of people have type O or Rh− factor.Part (a)Find the probability that a person has both type O blood and the Rh− factor.Part (b)Find the probability that a person does NOT have both type O blood and the Rh− factor.
Solution
Part (a) To find the probability that a person has both type O blood and the Rh− factor, we can use the formula for the probability of the intersection of two events:
P(A and B) = P(A) + P(B) - P(A or B)
Here, event A is the event that a person has type O blood and event B is the event that a person has Rh− factor.
P(A) = 0.41 (probability of having type O blood) P(B) = 0.15 (probability of having Rh− factor) P(A or B) = 0.47 (probability of having type O blood or Rh− factor)
Substituting these values into the formula, we get:
P(A and B) = 0.41 + 0.15 - 0.47 = 0.09
So, the probability that a person has both type O blood and the Rh− factor is 0.09 or 9%.
Part (b) The probability that a person does NOT have both type O blood and the Rh− factor is simply 1 minus the probability that a person has both. This is because the sum of the probabilities of all possible outcomes is always 1.
So, P(not A and B) = 1 - P(A and B) = 1 - 0.09 = 0.91
So, the probability that a person does NOT have both type O blood and the Rh− factor is 0.91 or 91%.
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