In this article we shall discuss the standard normal random variable calculator. Probability is defined as chance of occurrence of a certain event when it is expressed quantitatively. A standard normal random variable calculator computes the probability of one event and depends on probability of other related events.

**For an example:**

If you toss a coin, will you get a head or tail? The value of a probability is a number between 0 and 1 inclusive.

**Outcome:**

The ending result of an experiment.

**Example:**

Tossing a coin and the outcome would be someone of the two faces, H, T*.*

**Sample space(S):**

In each number of certain trials, the set of all probable outcomes is called the sample space.

**Example:**

When you roll a die, the sample space is:

S = {1, 2, 3, 4, 5, 6}

or

S = {1…6}

**Event: **

An event is the set of outcomes of a random occurrence, that is, a subset of a sample space.

**Independent variables:**

Independent variable concerned with decisive the probability of obtaining one event or another based upon a single draw.

P (A and B) = P (A). P (B)

**Dependent variables:**

Events are dependent means each probable outcome is related to the other. The two events A and B, the probability of obtaining simultaneously.

P (A and B) = P (A). P (B|A)

Usage of the standard normal random variable calculator to solving a probability problem:

- Identify the problem
- Examine data
- Report results

**Example 1:**

Bruce is running in two races 200-yard race and a 300-yard race. The probability of winning the 200-yard race is 0.25, and the probability of winning the 300-yard race is 0.50. The probability of winning at least one race is 0.75. What is the probability that Bruce will win both races?

**To find:** P (A ∩ B).

**Solution:**

**Step 1: ** Identify the problem.

Event A = Bruce wins the 200-yard race.

Event B = Bruce wins the 300-yard race.

**Step 2: **Examine data

P (A) = 0.25

P (B) = 0.5

P (A ∪ B) = 0.75

**Step 3:** To locate the above values in a standard normal random variable calculator: