Examples on Probability Formula

Example 1: Select a card at random from a standard deck. What is the probability of drawing a card with a feminine face?

Solution:

In a standard deck containing 52 cards: Total possible outcomes = 52

The number of favorable events (considering only queens as feminine faces) = 4

Therefore, the probability P(A) is calculated using the formula:

P(A) = Number of Favorable Outcomes ÷ Total Number of Outcomes

= 4/52

= 1/13.

Example 2: If the Probability of event E, denoted as P(E)=0.35, what is the probability of the complement event ‘not E’?

Solution:

Given that P(E)=0.35, we can use the complementary probability formula:

P(E) + P(not E) = 1

Substituting the known value:

P(not E) = 1 – P(E)

P(not E) = 1 – 0.35

Hence, P(not E) = 0.65

Example 3: Dangerous fires are very rare around 1% but the smoke is fairly common around 20% due to barbecues. Find the dangerous fire when 80% of dangerous fires produce smoke.

Solution:

Probability of dangerous Fire when there is smoke by using Bayes theorem:

P(Fire|Smoke) = {P(Fire)P(Smoke Fire)}/P(Smoke)

P(Fire)=0.01(1%) and P(Smoke|Fire)= 0.80 (80%), we can substitute these values:

P(Fire | Smoke)=( 0.02×0.90)/ 0.30

(Fire | Smoke)=0.018/0.30

(Fire | Smoke)= 0.06 = 6%.

Example 4: Within a bag, there are 2 green bulbs, 4 orange bulbs, and 6 white bulbs. When a bulb is randomly chosen from the bag, what is the probability of picking either a green bulb or a white bulb?

Solution:

Total number of bulbs in the bag is 2 green + 4 orange + 6 white = 12 bulbs

Number of green bulbs = 2, and the number of white bulbs = 6

Probability = (Number of green bulbs + Number of white bulbs) / Total number of bulbs

Probability = (2+6)/12

Probability = 8/12

Probability = 2/3.

Probability Formulas are important mathematical tools used in calculating the probability. Before knowing the probability formulas, we need to understand the concept of Probability in short. The possibility of the occurrence of a random event is defined by probability. A probability is a chance of prediction. Its applications extend across various domains including gaming strategies, the creation of forecasts based on probability in business, and the evolving field of artificial intelligence.

In this article, we will learn the meaning and definition of the Probability Formula and how to use these formulas in calculating Probability. We also see various terms related to Probability and different formulas to easily solve mathematical problems.