There are four basic blood groups: O, A, B and AB. Ordinarily anyone can receive
ID: 3062636 • Letter: T
Question
There are four basic blood groups: O, A, B and AB. Ordinarily anyone can receive the blood of a donor from their own group. Also, anyone can receive the blood of a donor from the O group, and any of the four types can be used by a recipient from the AB group. Any other combination causes problems. (a) Approximately 47% of New Zealanders have type O blood, 38% type A , 11% type B blood and and the rest have type AB blood. Let O be the event that a randomly selected New Zealander has type O blood and define events A, B and AB in a similar manner.
i. Write down P(O), P(A), P(B) and P(AB).
ii. Find P(Oc )
iii. Find P(B AB)
iv. What is the probability that a randomly chosen New Zealander would be able to donate blood to someone with type A blood?
Explanation / Answer
i. P(O) = 0.47
P(A) = 0.38
P(B) = 0.11
P(AB) = 1 - P(O) - P(A) - P(B)
= 1 - 0.47 - 0.38 - 0.11
= 0.04
ii. P(Oc) = 1 - P(O)
= 1 - 0.47
= 0.53
iii) P(B U AB) = P(B) + P(AB) - P(B and AB)
= 0.11 + 0.04 - 0
= 0.15
iv) P(a randomly chosen New Zealander would be able to donate blood to someone with type A blood) = P(the person chosen is having blood group A or O)
= 0.47 + 0.38
= 0.85
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