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2017 AMC 10A Problem 18

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2017 AMC 10A Problem 18AMC 10 Step by Step

Name: Date: September 13, 2026

Conditional Probability & States · difficulty 3 of 5 · about 4 min · position P16-20

Amelia has a coin that lands heads with probability $\tfrac{1}{3}$ , and Blaine has a coin that lands on heads with probability $\tfrac{2}{5}$ . Amelia and Blaine alternately toss their coins until someone gets a head; the first one to get a head wins. All coin tosses are independent. Amelia goes first. The probability that Amelia wins is $\tfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. What is $q-p$ ?

A)
$1$
B)
$2$
C)
$3$
D)
$4$
E)
$5$

2017 AMC 10A Problem 18

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