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A frog starts at “0” on a number line. Each second, it flips a fair coin,
and moves forward 1 unit if the coin shows heads, and forward 3
units if the coin shows tails. What is the probability that the frog will
eventually land on “8?” Express your answer as a common fraction.

 Oct 31, 2020
 #1
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What is the number of solutions to h + 3t = 8?

What is the probability that the frog goes over '8'? What happens if it gets three 3s?

Can you use modular arithmetic?

 

h+3t = 8

h = 2 (mod 3)

Let h be the number of heads.

Let t be the number of tails.

 

h = 3n + 2

so, t = 2-n

 

Ordered pairs of solutions:

(2, 2) ~ (5, 1) ~ (8, 0)

 

Non solutions that are greater than 8 but no extra leap over:

 

(0, 3) ~ (1, 3) ... count the rest, being mindful not to go an extra leap after you have reached >8.

 

Then answer is 3/ (non solutions + 3 )

 Oct 31, 2020

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