2

Part of 2016 AIME Problems

Problems(2)

Source: 2016 AIME I #2

Two dice appear to be standard dice with their faces numbered from

1

6

, but each die is weighted so that the probability of rolling the number

k

is directly proportional to

k

. The probability of rolling a

7

with this pair of dice is

\tfrac{m}{n}

m

n

are relatively prime positive integers. Find

m + n

AIME2016 AIME IDiceprobability

Source: 2016 AIME II #2

40\%

chance of rain on Saturday and a

30\%

of rain on Sunday. However, it is twice as likely to rain on Sunday if it rains on Saturday than if it does not rain on Saturday. The probability that it rains at least one day this weekend is

\frac{a}{b}

a

b

are relatively prime positive integers. Find

a+b