Difference between revisions of "2014 AMC 10B Problems"
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==Problem 25== | ==Problem 25== | ||
+ | In a small pond there are eleven lily pads in a row labeled <math>0</math> through <math>10</math>. A frog is sitting on pad <math>1</math>. When the frog is on pad <math>N</math>, <math>0<N<10</math>, it will jump to pad <math>N-1</math> with probability <math>\frac{N}{10}</math> and to pad <math>N+1</math> with probability <math>1-\frac{N}{10}</math>. Each jump is independent of the previous jumps. If the frog reaches pad <math>0</math> it will be eaten by a patiently waiting snake. If the frog reaches pad <math>10</math> it will exit the pond, never to return. what is the probability that the frog will escape being eaten by the snake? | ||
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+ | <math> \textbf {(A) } \frac{32}{79} \qquad \textbf {(B) } \frac{161}{384} \qquad \textbf {(C) } \frac{63}{146} \qquad \textbf {(D) } \frac{7}{16} \qquad \textbf {(E) } \frac{1}{2} </math> |
Revision as of 13:06, 20 February 2014
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
Problem 1
Leah has coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah's coins worth?
Problem 2
What is ?
Problem 3
Randy drove the first third of his trip on a gravel road, the next miles on pavement, and the remaining one-fifth on a dirt road. In miles how long was Randy's trip?
Problem 4
Susie pays for muffins and
bananas. Calvin spends twice as much paying for
muffins and
bananas. A muffin is how many times as expensive as a banana?
Problem 5
Problem 6
Orvin went to the store with just enough money to buy balloons. When he arrived, he discovered that the store had a special sale on balloons: buy
balloon at the regular price and get a second at
off the regular price. What is the greatest number of balloons Orvin could buy?
Problem 7
Suppose and A is $x%$ (Error compiling LaTeX. Unknown error_msg) greater than
. What is
?
Problem 8
A truck travels feet ever
seconds. There are
feet in a yard. How many yards does the truck travel in
minutes?
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Two concentric circles have radii and
. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
The numbers 1, 2, 3, 4, 5 are to be arranged in a circle. An arrangement is [i]bad[/i] if it is not true that for every from
to
one can find a subset of the numbers that appear consecutively on the circle that sum to
. Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there?
Problem 25
In a small pond there are eleven lily pads in a row labeled through
. A frog is sitting on pad
. When the frog is on pad
,
, it will jump to pad
with probability
and to pad
with probability
. Each jump is independent of the previous jumps. If the frog reaches pad
it will be eaten by a patiently waiting snake. If the frog reaches pad
it will exit the pond, never to return. what is the probability that the frog will escape being eaten by the snake?