How do you calculate chances with coin flips when you can choose to re-flip coins?

Each coin is independent of the other. So you can just focus on one coin for now, and figure out the probability of getting heads if you get 3 attempts)

P(coin lands on heads in 3 flips)

= P(heads on 1st flip) + P(tails on 1st flip, heads on 2nd) + P(tails on 1st and 2nd flip, heads on 3rd)

= (1/2) + (1/2)² + (1/2)³

= 7/8

P(all 3 coins land on heads with 3 attempts) = (7/8)³ = 343/512 = 0.669921875

mathmom says to start "= (1/2) + (1/2)² + (1/2)³"

is simply the sum of a geometric series

Have you learned about those yet?

and a simple formula exists for it

=a*((1-r^n)/(1-r))

a = (the first term)

r = (the "common ratio")

n = number of terms

This way, one does not have to do math the LONG WAY

of calculating many terms (increasing the error rate)

as a double-check

the formula you seek for the coin toss game is then

=[a*((1-r^n)/(1-r))]^c

c=number of coins = 3

a and r = 1/2

n = number of coin flips =3

calculator time:

Wolfram Alpha

((a (r^n - 1))/(r - 1))^c = 343/512

http://www.wolframalpha.com/input/?dataset=&equal=...

just change the value of n (number of flips)using Wolfram Alpha

and one can build a nice table of data (probabilities)

*****

I think this game would be way more fun with say

10 coins and toss all at once.

try to get a Yahtzee in 4 attempts (all 10 Tails or Heads)

of EITHER Tails or Heads

that requires a 'state' type solution (for probabilities)

transition matrix or recursion using Pascal's triangle

for example

thanks for the fun question!

A coin will get heads with a probabilty of ½.

So a coin will only flip three tails (so no heads) with a probability of (½)³ = ⅛, so ⅞ that it will turn up heads at least once in three flips.

So three coins will flip three heads in at most three flips (original flip and up to two reflips if requred) with a probability of 3C3 (⅞)³ (⅛)⁰ = 343/512

The "chance" a coin will land either heads or tails is always the same: 50/ 50.

The probability a coin will land either heads or tails is a completely different thing.