SAT question d4413871 (Probability And Conditional Probability)

Question

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 1/9 . What is the value of x ?

College Board · Accepted Answer

The correct answer is 8. The correct answer is 8 . In this group, 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, 2/(7 + 2 + 1 + x) = 1/9 . Combining like terms on the left-hand side of the equation yields 2/(10 + x) = 1/9 . Multiplying both sides of this equation by 9 yields (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 .

CookSAT · Answer

Note: The denominator counts all rhesus-negative people, so fitting the given conditional probability gives x=8.

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

Explanation

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SAT Question d4413871: Probability And Conditional Probability answer and explanation with Desmos solution

Explanation

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