# What is the chance of getting 5 tails on 10 tries? **URL:** \ **Category:** Factual Questions\ **Created:** [December 25, 2020, 12:05pm UTC](https://boards.straightdope.com/t/what-is-the-chance-of-getting-5-tails-on-10-tries/928883 "2020-12-25T12:05:38Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![Loggins](https://avatars.discourse-cdn.com/v4/letter/l/74df32/32.png) [@Loggins](https://boards.straightdope.com/u/Loggins)\ **Post date:** [December 25, 2020, 12:05pm UTC](https://boards.straightdope.com/t/what-is-the-chance-of-getting-5-tails-on-10-tries/928883/1 "2020-12-25T12:05:38Z")
Spinning off this debate; > [@Settle an argument, a 1 in 100 chance of something happening, happens 30 times. Is it basically around a 30% chance of occuring?](https://boards.straightdope.com/t/settle-an-argument-a-1-in-100-chance-of-something-happening-happens-30-times-is-it-basically-around-a-30-chance-of-occuring/928520): > > I know I’m severely simplifying it but looking up the math online it seems like it’s basically a 28% chance rounded down, but my friend is arguing with me about gamblers fallacy and how the actual odds are significantly lower. And now he’s arguing with me about how flipping a coin 10 times doesn’t automatically mean 50% of the time the coin will land heads. His entire argument is that instead of 30% chance, I should be calculating it like it’s a 10% chance. Who’s right? What is the chance of getting 5 of each when flipping a coin? Im pretty sure its rare? Although it should be the norm? Im all question marks, so have at it. ---
**Author:** ![CardboardBoxx](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cardboardboxx/32/7079_2.png) [@CardboardBoxx](https://boards.straightdope.com/u/CardboardBoxx)\ **Post date:** [December 25, 2020, 12:15pm UTC](https://boards.straightdope.com/t/what-is-the-chance-of-getting-5-tails-on-10-tries/928883/2 "2020-12-25T12:15:20Z")
The odds are `(5!*5!)/10!)/10^2` =252/1024= about 24.6% 5! means `1*2*3*4*5`, there are 252 paths to get 5 spins of each from 1024 total paths. ---
**Author:** ![CardboardBoxx](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cardboardboxx/32/7079_2.png) [@CardboardBoxx](https://boards.straightdope.com/u/CardboardBoxx)\ **Post date:** [December 25, 2020, 12:25pm UTC](https://boards.straightdope.com/t/what-is-the-chance-of-getting-5-tails-on-10-tries/928883/3 "2020-12-25T12:25:28Z")
Note I accidentally transposed the expression, it should be (10!/(5!\*5!))/10^2 ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [December 25, 2020, 12:48pm UTC](https://boards.straightdope.com/t/what-is-the-chance-of-getting-5-tails-on-10-tries/928883/4 "2020-12-25T12:48:25Z")
> [@CardboardBoxx](#): > > (10!/(5!\*5!))/10^2 You transposed the bottom, too: 2^10, not 10^2. My post from another thread may be helpful as well: If you want a reasonably simple method to calculate other heads/tails results: If you flip n coins, expand (H+T)^n. If you want to know the probability of x heads and n-x tails, look for the H^x T^(n-x) in your expansion. Isolate it, plug in your probabilities for both H and T (50% of each if they are fair coins (and by the way, all the coins need to have the same bias for this method to work: For example if one coin is biased 70% H, 30% T, then all coins must have that same probability)) and the result is the probability you want. For example, with three coins: (H+T)^3 = H^3 + 3H^2 T + 3H T^2 + T^3. Assuming the coins are all fair, the probability of flipping 2 heads, 1 tail would be 3H^2 T = 3(.5)^2 (.5) = 37.5%. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [December 25, 2020, 4:13pm UTC](https://boards.straightdope.com/t/what-is-the-chance-of-getting-5-tails-on-10-tries/928883/5 "2020-12-25T16:13:28Z")
The graph shown here shows the probability of each number of heads, from 0 to 10: > **[Desmos | Graphing Calculator](https://www.desmos.com/calculator/g7dhqfhdsc)** > > Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.