# Toss of three coins - probability

Assume all outcomes are equally probable, ie. consider the uniform probability measure on the probability space.

I need to determine the following:

1. How many outcomes are there in a toss of three coins?\

Let 0 denote heads and let 1 denote tails.

$E=\{(c_1,c_2,c_3)\in\mathbb{R}^3|e_i\in{0,1},i=1,2,3\}$.

$\#E=2^3=8$.

1. The probability that all coins show heads.

2. The probability that at least two coins show tails.

3. The probability that precisely one coin show tails.

4. What are the answers to 1-4 for a toss of $n$ coins? How big must $n$ be to ensure that the probability that at least one of the coins er greater than $95\%$?

• $8$ is a good answer if you want the outcomes to be equally probable to help answer questions 2,3,4 – Henry Nov 3 '15 at 0:06
• The first part of my question was wrongly formulated, updated now. – jukka.aalto Nov 3 '15 at 0:09
• @Henry It is mainly the following questions that I'm concerned with. – jukka.aalto Nov 3 '15 at 7:52

• $8$ outcomes: HHH, HHT, HTH etc;
• $4$ outcomes: number of heads is $0,1,2,3$;
• $2$ outcomes: more heads or more tails;
• $2$ outcomes: second toss is heads or tails
• $3$ outcomes: number of tails is less than $1$, equal to $1$, greater than $1$;
• $6$ outcomes: the number of heads if the first two tosses count double is $0,1,2,3,4,5$;