coin toss probability

We throw the coin 1 000 000 times. How many times on average will make 13 successful heads? Now the problem with the naive: 1 000 000/(2^13) is that once it made 13 heads the 14 head will happen with 1/2 probability , but it will count as 2 13 successful heads. 15 will happen 4xtimes less, but...

Alan, Bob, and Charlie agreed that the “odd man” (the person whose outcome is different from others) would buy the coffee. After simultaneously flipping their coins, Bob turned up with the only “tail”. At this point Bob demanded to Alan’s and Charlie’s coins. He discovered that Alan had used...

I have a coin that lands heads with probability p1; you have a coin that lands heads with probability p2. I toss my coin until I get a head. Each time I toss my coin you toss your coin. Let X denote the number of tosses I take to get the head and Y denote the number of heads you get. (a) Find...