MathDB

10. Prair picks a three-digit palindrome

n

at random. If the probability that

2n

is also a palindrome can be expressed as

\frac{p}{q}

in simplest terms, find

p + q

. (A palindrome is a number that reads the same forwards as backwards; for example,

161

and

2992

are palindromes, but

342

is not.)
11. If two distinct integers are picked randomly between

1

and

50

inclusive, the probability that their sum is divisible by

7

can be expressed as

\frac{p}{q}

, where

p

and

q

are relatively prime positive integers. Find

p+q

.
12. Ali is playing a game involving rolling standard, fair six-sided dice. She calls two consecutive die rolls such that the first is less than the second a "rocket." If, however, she ever rolls two consecutive die rolls such that the second is less than the first, the game stops. If the probability that Ali gets five rockets is

\frac{p}{q}

, where

p

and

q

are relatively prime positive integers, find

p+q

R4

Problems(1)