# Probability of $6$ and $7$ tails in a row in 24 flips of a biased coin

Suppose you are flipping a coin with probability of Heads being 0.4931 and Tails being 0.5069

Can someone please tell me what is the probability of hitting 6 and 7 tails in a row in 24 tries? how about 44 tries?

OK. I have been asked to edit my question! Here is the story:

The game "Baccarat" in casinos is very much like flipping a coin. the outcome is either "banker", "player" or Tie. If you disregard ties, the probability of banker win is 0.5069 and player win is 0.4931. I am betting in a way that every loss is covered by an eventual win. But if there are 7 losses in a row, i do not play any more. I usually play 20 hands to win 100$. I wanted to know what is the probability of my loss. I hope the critics are now satisfied with the reason behind my question! • It's but a binomial distribution. – Asydot Sep 5 '15 at 20:44 • Your question will likely be reopened, but for the future you should note that adding context to your question includes adding "your thoughts on the problem and any attempts you have made to solve it", as stated in the reason your post was put on hold. – Mike Pierce Sep 6 '15 at 7:40 • – rubik Jul 31 '16 at 2:14 ## 3 Answers For$k$times in$n\$ trials: $$p = {n \choose k} (0.4139)^{n-k}(0.5069)^k$$

These are called Bernoulli trials, and this probability distribution is called the binomial distribution.

• Thanks BolzWeir. But are you sure it gives me the probability of k tails "in a row"? I tried to solve it for 40>n>k but as I increase the number of tries, probability decreases. Having a probability if 1.8e-5 for flipping a coin 40 times and getting 7 tails in a row sims too small to me. – Danny Sep 5 '15 at 23:08
• No, the binomial distribution counts the total number of successful trials, not necessarily in a row. – rubik Jul 31 '16 at 2:12

I recently asked a similar question here:

Coin flipping - likely to hit 7 heads or tails in a row (answered) and betting progression

In my question I tried to find out how probable I would get tails 7 times in a row if tails came up 60% of the time in a single flip.

What I found out is that in any 7 flips of the coin there is about 3% chance that it would come up tails 7 times in a row. And that after 128 and nearing 254 flips of the coin I would be expecting tails to happen 7 times in a row.

In just 24-44 flips you should have little chance of tails coming up 7 times in a row. Especially if your odds are closer to 50 50 as you said.

In 24 flips, probability of getting 6 tails in a row: You can either get all tails in flips 1,2,3,4,5,6 or flips 2,3,4,5,6,7 or flips 3,4,5,6,7,8 or flips 4,5,6,7,8,9 or flips 5,6,7,8,9,10 to flips 19,20,21,22,23,24. If you could all of the possibilities you get 19. So you choose one case from 19 which is $${19 \choose 1}$$ and the probability of all of these to be tails is $$(0.5069)^6$$ So the answer should be $${19 \choose 1}*(0.5069)^6$$