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  Blood type
Rhesus factor  A B AB O
+ 33 9 3 37
- 7 2 1 x


Human blood can be classified into four common blood types—A, B, AB, and O. It is also characterized by the presence (+) or absence (-) of the rhesus factor. The table above shows the distribution of blood type and rhesus factor for a group of people. If one of these people who is rhesus negative (-) is chosen at random, the probability that the person has blood type B is \(\frac{1}{9}\). What is the value of x ?

  1. 8
  2. 1
  3. 3
  4. 5

Answer (Detailed Solution Below)

Option 1 : 8

Detailed Solution

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The correct answer is 8. In this group, \(\frac{1}{9}\) of the people who are rhesus negative have blood type B. The total number of people who are rhesus negative in the group is 7 + 2 + 1 + x, and there are 2 people who are rhesus negative with blood type B. Therefore, \(\frac{2}{(7+2+1+x)}=\frac{1}{9}\). Combining like terms on the left-hand side of the equation yields \(\frac{2}{(10+x)}=\frac{1}{9}\). Multiplying both sides of this equation by 9 yields \(\frac{18}{(10+x)}=1\), and multiplying both sides of this equation by (10 + x) yields 18 = 10 + x. Subtracting 10 from both sides of this equation yields 8 = x. 
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