Question

1. all human blood can be classified as o, a, b or ab. in addition, the frequency of the occurrence of these blood types varies by ethnic and racial groups. according to stanford university, these are the probabilities of human blood types in the united states (the probability for type a has been omitted on purpose):

o	a	b	ab

if a person in the united states is chosen at random,
a) what is the probability of the person having blood type a?
b) what is the probability of the person having blood type a or b?
c) what is the probability of the person not having blood type a or o?

Explanation:

Step1: Find probability of blood - type A

The sum of probabilities of all blood - types is 1. Given probabilities of O, B, and AB are 0.44, 0.10, and 0.04 respectively. Let the probability of A be $P(A)$. Then $P(A)=1-(0.44 + 0.10+0.04)=1 - 0.58 = 0.42$.

Step2: Find probability of A or B

The probability of two mutually - exclusive events $A$ and $B$ is given by $P(A\cup B)=P(A)+P(B)$. We know $P(A) = 0.42$ and $P(B)=0.10$. So $P(A\cup B)=0.42 + 0.10=0.52$.

Step3: Find probability of not A or O

First, find the probability of A or O, $P(A\cup O)=P(A)+P(O)=0.42 + 0.44 = 0.86$. Then the probability of not A or O is $1 - P(A\cup O)=1 - 0.86 = 0.14$.

Answer:

a) 0.42
b) 0.52
c) 0.14