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Problem-Solving and Data Analysis Difficulty: Hard

	Blood type
Rhesus factor	A	B	AB	O
$plus$	33	9	3	37
$minus$	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 $open parenthesis, plus, close parenthesis$ or absence $open parenthesis, minus, close parenthesis$ 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 $open parenthesis, minus, close parenthesis$ is chosen at random, the probability that the person has blood type B is $one ninth$ . What is the value of x ?

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Explanation

The correct answer is 8. In this group, $one ninth$ of the people who are rhesus negative have blood type B. The total number of people who are rhesus negative in the group is $7 plus 2, plus 1, plus x$ , and there are 2 people who are rhesus negative with blood type B. Therefore, $the fraction with numerator 2, and denominator, 7 plus 2, plus 1, plus x, end fraction, equals one ninth$ . Combining like terms on the left-hand side of the equation yields $the fraction with numerator 2, and denominator, 10 plus x, end fraction, equals one ninth$ . Multiplying both sides of this equation by 9 yields $the fraction with numerator 18, and denominator, 10 plus x, end fraction, equals 1$ , and multiplying both sides of this equation by $open parenthesis, 10 plus x, close parenthesis$ yields $18 equals, 10 plus x$ . Subtracting 10 from both sides of this equation yields $8 equals x$ .