# flipping

1. ### Flipping between p-adics and reals

Let x\in \mathbb{Q}_p. We can represent x by the p-adic series x=\sum_{n\ge k}a_np^n, k,a_n \in \mathbb{Z}, 0\le a_n < p. Define f_p:\mathbb{Q}_p \to \mathbb{R} by f_p(x) = \sum_{n \le -k}a_{-n} p^{-n-1} (essentially flipping the digits across the decimal point). Define the relation \sim by...
2. ### Flipping coin

We flip a a biased coin 100 times. p=probability of head q=1-p= probability of tail. Let us call the longest run of heads LH and the longest run of tails LT. We define a random variable X=min(LT,LH) and Y=LH+LT. What are the probability laws of X and Y? Thank you for any help. Ps : It is not a...
3. ### Expected number of turns in single player coin flipping game

Similar to my other topic, again I play a coin flipping game. This time I start with zero points. I repeatedly flip a coin. Heads = I get one point, tails = I lose one point. My score can also be negative. Question: what's the expected number of turns I have to take, to reach 3 points?
4. ### Probability and expected number of turns in coin flipping game?

Suppose we play a coin game: we flip a coin, upon tails you get one dollar from me, upon heads I get one dollar from you. We repeat this until one of us is broke. Now, at the beginning of the game, I have $4 and you have$6. 1. What is the chance of me winning the game? (thus ending up...
5. ### Flipping coins

I'm trying to write out the following Bernoulli Space events in terms of E_n \Omega = \{ \omega = \omega_1 \omega_2 \omega_3 \ldots : \omega_n = 1,0 \} (i) exactly 2 heads are obtained. E_x=\{ \omega \in \Omega : \omega_x=1 \} E_y=\{ \omega \in \Omega : \omega_y=1 \} E_z= \{\omega \in...
6. ### tricky biased coin flipping question

I'm having trouble with the following question; "A biased coin is tossed until more heads then tails appear. The coin is biased such that it lands on heads with probability 2/3 and tails with probability 1/3 What is the expected number of flips and the variance?" Any help would be...

What's the probability of flipping n consecutive heads on a fair coin? What about an even number of consecutive heads? For the first one, I simply got (1/2)^n, is this correct? How will I solve the second? Any hints? There could be infinite number of arrangements as there are infinite...
8. ### probability/combination flipping a coin.

question is, If you flip a coin 5 times what is the probability of getting 4 heads, and 1 tails? total number of outcomes is 2^5 because you flip a coin there are to possible outcomes 5 times. Since there is no order it is a combination *this is where I am confused* I thought when you have two...
9. ### flipping the inequality sign

When working with inequalities, what are the rules for flipping the ineqaulity sign around when you move the variable around. I know when dividing by a negative we flip. Do we flip the sign around so that it is always oriented with the same orientation it began as. Since the variable could be...
10. ### flipping number question..

what is the math formula(algorithm) for flipping any number like: 47->74 1655 -> 5561 12345->54321 1190 -> 911 ??

14. ### Flipping Coins

There is a gambling game that goes like this, you place a $5 bet to begin with. A coin is then flipped until it flips tails (or the house maximum of x flips). Each time it lands on heads the house pays an amount equal to$1 times the number of consecutive flips, for example, land three heads in...