Q:

The probability is? Please help

Accepted Solution

A:
The sum of the probabilities in a probability distribution is always 1.
A probability distribution is a collection of probabilities that defines the likelihood of observing all of the various outcomes of an event or experiment. Based on this definition, a probability distribution has two important properties that are always true:
Each probability in the distribution must be of a value between 0 and 1.
The sum of all the probabilities in the distribution must be equal to 1.
An example: You could define a probability distribution for the observation for the number displayed by a single roll of a die. The probability that the die with show a "1" is
1
6
.
That's because there are six possible outcomes, and only one of those outcomes is a "1". Lets label the probabilities of all the possible outcomes for the single die.
Roll a "1": Probability is
1
6

Roll a "2": Probability is
1
6

Roll a "3": Probability is
1
6

Roll a "4": Probability is
1
6

Roll a "5": Probability is
1
6

Roll a "6": Probability is
1
6
Each probability is between 0 and 1, so the first property of a probability distribution holds true. And the sum of all the probabilities:
1
6
+
1
6
+
1
6
+
1
6
+
1
6
+
1
6
=
1
,
so the second property of a probability distribution holds true.