91Ó°ÊÓ

When we talk about independent events in probability, we mean that the occurrence or non-occurrence of one event does not affect the likelihood of the other event happening. Independent events are evaluated using multiplication of probabilities.
For example, in the given problem, the events of being bitten by a tick are independent because being bitten once and contracting Lyme disease does not influence the chance of getting the disease from a second bite.
Think of it like flipping a coin. Each coin flip is independent—heads or tails. The outcomes of previous flips (like many bites by ticks) do not alter the likelihood of future outcomes.
This concept tells us that the probability of multiple independent events all occurring is the product of the probabilities of each individual event. In the exercise, the first and second tick bites are seen as independent. Thus, we find the probability of not getting the disease first and getting it second by multiplying their individual probabilities. It drives home the idea that each tick interaction is a separate instance of chance.

Fractions are a way to represent numbers that are not whole, often conveying probability and ratios. In probability, a fraction consists of a numerator and a denominator.
In the provided exercise, the probability of contracting Lyme disease from a single tick bite is represented as the fraction \( \frac{1}{100} \). This tells us that out of every 100 tick bites, you might expect to get Lyme disease 1 time.
Likewise, the probability of not contracting the disease from the first bite is calculated as \( 1 - \frac{1}{100} = \frac{99}{100} \). This fraction further communicates that, in most cases (99 out of 100 times), a tick bite does not lead to Lyme disease.
Understanding fractions in probability helps to clearly express the likelihood of events. They serve as useful mathematical tools to convey precise chances, especially when used to communicate the odds of events like the scenarios described in the exercise.

Tackling probability problems through a step-by-step approach allows us to clearly reason through each part of the problem without missing any detail. Let's break down the current exercise with this method.

• Step 1: Identify the probability of not getting infected from one bite. We begin with understanding the probability of contracting Lyme disease from one bite, which is \( \frac{1}{100} \). Therefore, the probability of not getting infected from one bite would be \( 1 - \frac{1}{100} = \frac{99}{100} \).


• Step 2: Calculate the probability of not getting infected from the first bite and contracting the disease from the second. Here, two independent events need to be considered sequentially. The first event is not contracting the disease, given by \( \frac{99}{100} \). The second event is getting the disease from the next bite, which is \( \frac{1}{100} \). To find the combined probability of these independent events occurring in this sequence, multiply the two results: \( \frac{99}{100} \times \frac{1}{100} = \frac{99}{10000} \).

This methodical approach helps manage complex problems and ensures that each part is thoroughly evaluated, leading to a clear and accurate solution.