what is probability with two outcomes?

Answer 1

thinking a coin toss, there are only two outcomes: head and tails.
therefore, the probability you haing head once

1/2(50%).........

Answer 2

Joint probability. For example, what is the joint probability of rolling a 1 and a 6 on one roll of two dice.

The 1 and 6 are the two target outcomes...that make up the point. That's written as P(1 and 6) = n(1)/6 X n(6)/6 + n(6)/6 X n(1)/6 = 2[n(1)/6 X n(6)/6]; where n(x) means the number of ways to get x value and the /6 in each factor means there a six possible outcomes (1,2,3,4,5,6) when rolling each dice.

There are two terms, n(1)/6 X n(6)/6 + n(6)/6 X n(1)/6, that look almost alike because we could roll 1 and 6 two ways. We could roll 1 on the red dice and 6 on the blue one, OR 1 on the blue dice and 6 on the red one. The "OR" signifies two terms are required. OR in words is like having a "+" sign in arithmetic.

Thus, P(1 and 6) = 2[1/6 X 1/6] = 1/18 for the joint probability of the two outcomes...1 and 6.

Here's another one...what's the probability of the next president of the U.S. being a democrate and a woman? Suppose there are 3 demos of which one is a woman, and 3 republicans of which none is a woman.

So the joint probability of electing a demo who is also a woman is P(D and W) = n(D and W)/6 = 1/6. We can see this from the following table, which shows each candidate as equally likely:

.....D.....R
W..1.....0
M...2.....3

The D and R columns are demos and republicans; the rows W and M are women and men. We see there are N = 6 possible outcomes for the election, but n(D and W) = 1, only one is both demo and woman.

We can also get P(D and W) by say P(D) = 1/2 and if a demo is elected the probability it will be a woman is P(W|D) = 1/3. We read P(W|D) as the probability of a woman "given" a demo is elected. Thus, P(D and W) = P(D) X P(W|D) = 1/2 X 1/3 = 1/6, which thankfully, is the same answer we got above.

Answer 3

a coin toss.