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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.

Verified Answer :

The solution to the problem is as follows:

P(O∪Rh−)=0.45


Additive Law of Probability

P(A∪B)=P(A)+P(B)−P(AB)


Therefore,

P(OandRh−)=P(O)+P(Rh−)−P(O∪Rh−)=0.49+0.15−0.45=0.19

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Answer:

Probability of a person having both type O blood and the Rh− factor is \(19\)%

Explanation:

The probability of a person having O blood group is \(0.49\)

The probability of a person having Rh- factor  is \(0.15\)

The probability of a person having either O blood group or Rh- Factor is \(0.45\)

Hence, As per the additive rule of probability

Probability of event A and B together \(=\) Probability of A \(+\) Probability of A \(-\) probability of either A or B

Here event A is occurrence of O blood group

event B is occurrence of Rh- factor

Substituting the given values in above equation, we get -

Probability of a person having both type O blood and the Rh− factor \(= 0.49 + 0.15 -0.45\\= 0.19\)