Applications of probability

In areas where statistical analysis is based, probability is used to predict uncertainty, make estimates, and predict the results of research investigations. Prediction and estimation help in decision-making and hence planning and controlling for the future.

Below are some examples of problems handled using probability:

1. Cyclists trying to minimize the chance of accidents check if bicycle parts are in good order and consider other significant causes of accidents.
2. Campaign managers for political parties use results from recent polls to estimate their candidate's chance of winning an election.

These applications affect decisions about health, citizenship, parenthood, jobs, financial concerns, and many other important matters. Today, an informed person must understand data and make intelligent decisions based on quantitative arguments involving uncertainty or chance.

Example 1

The success of a small poultry project depends on the availability of good rationed feed and heat for the chicks. The probability of the availability of good rationed feed, heat, and starting capital is 0.52. If the probability of success with good rationed feed and heat given that starting capital is available is 0.85, find the probability of the availability of the starting capital.

Solution:

The availability of good rationed feed and heat depends on the availability of capital. Thus, these are dependent events.

Let $A$ be the event that good rationed feed and heat are available, and $B$ be the event that starting capital is available. Then, $P(A \cap B) = 0.52$. The conditional probability $P(A|B) = 0.85$. We need to find $P(B)$.

$P(A|B) = \frac{P(A \cap B)}{P(B)}$

Therefore,

$P(B) = \frac{P(A \cap B)}{P(A|B)}$

$P(B) = \frac{0.52}{0.85}$

$P(B) \approx 0.61$

Therefore, the probability of the availability of starting capital is approximately 0.61.