Formulas: Probability

# Formulas: Probability | Quantitative Aptitude for SSC CGL PDF Download

## Formula & Definition for Probability

• Probability is a numerical representation indicating the likelihood or possibility of a specific event occurring.
• Probability signifies the degree to which events happen. When events occur, such as throwing a ball or selecting a card from a deck, there is a corresponding probability associated with each event.
• In mathematical terms, probability is defined as the ratio of favorable outcomes to the total number of possible outcomes. The theory of probability encompasses three approaches: the Classical Approach, Relative Frequency Approach, and Subjective Approach.

## Basic Definition and Formula

• Random Event: If an experiment is repeated numerous times under similar conditions and does not yield the same result each time, but the outcome in a trial is one of several possible outcomes, then such an experiment is termed a random event or a probabilistic event.
• Elementary Event: The elementary event represents the outcome of each occurrence of a random event. Whenever the random event takes place, each corresponding outcome is referred to as an elementary event.
• Sample Space: The sample space denotes the set of all conceivable outcomes of a random event. For instance, when a coin is tossed, the potential outcomes are heads and tails.
• Event: An event is a subset of the sample space associated with a random event.
• Occurrence of an Event: An event linked to a random event is considered to occur if any of the elementary events within it is an actual outcome.

## Basic Probability Formulas

• Probability Range – 0 ≤ P(A) ≤ 1
• Rule of Complementary Events – P(AC) + P(A) =1
• Rule of Addition – P(A∪B) = P(A) + P(B) – P(A∩B)
• Disjoint Events – Events A and B are disjoint if P(A∩B) = 0
• Conditional Probability –
• Bayes Formula –
• Independent Events – Events A and B are independent if. P(A∩B) = P(A) ⋅ P(B).

### Sample Probability Based Questions

Q1: In a bag, there are 7 red marbles, 5 blue marbles, and 4 green marbles. Two marbles are randomly selected from the bag without replacement. What is the probability that both of them are blue?
Sol:
For the first draw, Probability of selecting a blue marble is 5/16 (5 blue marbles out of 16 total marbles).
After the first marble is drawn, there are 4 blue marbles left out of 15 total marbles.
For the second draw, the probability of selecting a blue marble is 4/15.
To calculate the probability of both marbles being blue =>
Probability = 20/24 = 1/22

Q2: In a bag, there are 3 green bulbs, 4 orange bulbs, and 5 white bulbs. A bulb is randomly picked from the bag. What is the probability of selecting either a green bulb or a white bulb?
Sol:
Total number of bulbs in the bag is 3 green + 4 orange + 5 white = 12 bulbs
Number of green bulbs is 3, and the number of white bulbs is 5
Probability of selecting either a green or a white bulb, we add the number of green bulbs and the number of white bulbs, and then divide it by the total number of bulbs.
Probability = (Number of green bulbs + Number of white bulbs) / Total number of bulbs

Probability = 8/12
Probability = 2/3

Q3: Joey Tribbiani organized a rack race with two participants. The probability of the first participant winning is 2/7, and the probability of the second participant winning is 3/5. What is the probability that one of them will win?
Sol:
Let’s denote:
P(A) = Probability of the first participant winning = 2/7
P(B) = Probability of the second participant winning = 3/5
The probability of both participants winning simultaneously (a tie) is zero since there can only be one winner. Therefore, the probability that one of them will win is:
P(one of them wins) = P(A) + P(B) – P(A and B)
P(one of them wins) = P(A) + P(B) – 0 (since P(A and B) = 0)
P(one of them wins) = P(A) + P(B)
Substituting the given probabilities:

Q4: In a drawer, there are 4 black pens, 3 blue pens, and 5 red pens. A pen is drawn at random from the drawer. What is the probability that it is either black or blue?
Sol:
We have calculate the probability of drawing a black or blue pen from the drawer
The total no. of pens in the drawer is 4 black + 3 blue + 5 red = 12 pens
Probability of drawing a black pen is 4/12
Probability of drawing a blue pen is 3/12 = 1/4
Hence, The probability of drawing either a black or blue pen, we add the individual probabilities:
Probability = 4/12 + 3/12
Probability 7/12

Q5: Sylvester Stallone brought a box of balloons for a group of students. The box contains 3 balloons of Shape A, 4 balloons of Shape B, and 5 balloons of Shape C. If three balloons are randomly drawn from the box, what is the probability that all three balloons are of different shapes?
Sol:
Total No. of Balloons = 3 Balloons of Shape A +4 Balloons of Shape B + 5 Balloons of Shape C = 12
n(s)= 12C= 220
n(e)= 3C4C5C60
P= 60/220 = 3/11

The document Formulas: Probability | Quantitative Aptitude for SSC CGL is a part of the SSC CGL Course Quantitative Aptitude for SSC CGL.
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## FAQs on Formulas: Probability - Quantitative Aptitude for SSC CGL

 1. What is the definition of probability?
Ans. Probability refers to the likelihood or chance of an event occurring. It is a numerical measure that ranges from 0 to 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.
 2. How is probability calculated?
Ans. Probability can be calculated using the formula: Probability = Number of favorable outcomes / Total number of possible outcomes This formula is applicable when all outcomes are equally likely.
 3. Can the probability of an event be greater than 1?
Ans. No, the probability of an event cannot be greater than 1. The maximum value of probability is 1, which indicates certainty. If the calculated probability exceeds 1, it suggests an error in the calculation.
 4. What is the meaning of mutually exclusive events in probability?
Ans. Mutually exclusive events are events that cannot occur simultaneously. If one event happens, the other event cannot happen at the same time. For example, when flipping a coin, the outcomes of getting a head and getting a tail are mutually exclusive events.
 5. How do you calculate the probability of independent events?
Ans. The probability of independent events can be calculated by multiplying the probabilities of each event. For example, if the probability of event A is 0.6 and the probability of event B is 0.3, then the probability of both events occurring is 0.6 * 0.3 = 0.18.

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