Discrete Mathematics Week11 Probability

Probability is a fundamental concept in mathematics and statistics that quantifies the likelihood or chance of an event or outcome occurring. It is a measure that assigns a numerical value between 0 and 1 to the likelihood of an event, where:

0 indicates an impossible event, meaning it will not occur.
1 indicates a certain event, meaning it will definitely occur.
In between 0 and 1, probabilities represent the degree of uncertainty or the likelihood of different outcomes. The higher the probability, the more likely an event is to occur.

Example: Coin Toss Probability

Suppose you have a fair, unbiased coin. When you toss this coin, it can land in one of two possible outcomes: heads (H) or tails (T). The probability of getting heads (H) or tails (T) in a single coin toss is 0.5 or 50%.

In this case:

The sample space (all possible outcomes) is {H, T}.
The probability of getting heads (H) is P(H) = 0.5.
The probability of getting tails (T) is P(T) = 0.5.
Now, if you want to find the probability of getting heads (H) twice in a row when you toss the coin two times, you can use the multiplication rule for independent events. Since each toss of the coin is independent of the previous toss, you can calculate the probability by multiplying the individual probabilities:

P(H, H) = P(H) * P(H) = 0.5 * 0.5 = 0.25

So, the probability of getting heads (H) on two consecutive coin tosses is 0.25, or 25%.

This example illustrates how probability is used to assess the likelihood of events occurring in simple scenarios, such as coin tosses. In more complex situations, probability helps us make informed decisions, understand risk, and analyze data in various fields, including statistics, finance, and science.