Question blood-

3.5 Probability & Conditional Probability - Conditional probability formula
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 Blood type   
Rhesus factorABABO
plus339337
minus721x

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 ?

Enter your answer:

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

Hard-difficulty · SAT Math · Probability & Conditional Probability — Conditional probability formula. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer 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.