Probability Definition: 

Probability is a measure of the possibility that an event will occur. Many events cannot be planned with absolute accuracy. We can only predict the likelihood of an event occurring by using it. Probability can range from 0 to 1, with 0 indicating that the event is impossible and 1 indicating that it is certain. Probability is a crucial topic for aspirants , as it explains all of the fundamental principles. The probability of all events in a sample space equals to one.

Formula for Probability:

The probability formula implies that the probability of an event occurring equals the ratio of the number of favorable outcomes to the total number of outcomes.

$$ Probability \ of \ the \ event \ happening \ P(E) = \frac{number \ of \ favorable \ outcomes} { total \ number \ of \ outcomes}$$

Terminology for Probability Theory:

The following probability theory words helps in better understanding of the ideas of probability.

An experiment is defined as a trial or activity that produces an outcome.

Sample Space: A sample space is the set of all probable experimental outcomes. The sample space for flipping a coin is {head, tail}.

Favorable Outcome: A good outcome is an event that produces the desired or expected event. For example, if we roll two dice, the possible/favorable outcomes for receiving the sum of the numbers on the dice as 4 are (1,3), (2,2), and (3,1).

Probability of an event:
Assume that an event E can occur in r out of n probable or equally likely ways. Then the chance of the event occurring or its success is represented as: P(E) = r/n

The likelihood that the event will not occur, often known as failure, is stated as:

P(E’) = (n-r)/n = 1-(r/n).

E’ indicates that the event will not occur.

So, now we can say:

P(E) + P(E’) = 1

This signifies that the sum of all probability in a random test or experiment equals 1.

Practice Quizzes

Probability Quiz 1 – Coming Soon

Probability Quiz 2 – Coming Soon

Probability Quiz 3 – Coming Soon

Examples Problems

Q1. A box contains 3 Avocado and 2 Olives. If two fruits are picked at random, then what is the probability that is at least one Avocado in the drawn fruits?

1. 9/10
2. 4/5
3. 7/10
4. 3/5
5. None of these

Ans – Answer: A
Required probability = (3C₁ * 2C₁ + 3C₂)/5C₂
= [(3 * 2) + 3]/(5 * 2)
= 9/10

Q2. A bag contains 60 box’s marked from 1 to 60. If one box is drawn at random, then what is the probability that is marked with a number divisible by 7?

1. 1/15
2. 2/15
3. 1/5
4. 4/15
5. None of these

Ans – Answer: B

Number of marked box divisible by 7 = 7, 14, 21, 28, 35, 42, 49, 56
Required probability = 8/60 = 2/15

Q3. A box contains 6 Pink balls, 3 black balls, 4 orange balls and 2 white balls. If four balls are drawn out randomly, then the probability of getting balls of different colour?

1. 11/135
2. 48/455
3. 23/479
4. 34/477
5. None of these

Ans – Answer: B
Total probability n(S) = 15C₄ = (15*14*13*12) / (1*2*3*4)
Required probability n(E) = 6C₁ and 3C₁ and 4C₁ and 2C₁
P(E) = n(E)/n(S)
P(E) = (6C₁ and 3C₁ and 4C₁ and 2C₁) / 15C₄
P(E) = 48/455

Q4. A box contains red and green balls and the total number of balls in the box is 15. If the probability of picking a green ball is 0.4, find the number of red balls from the box?

1. 8
2. 7
3. 9
4. 6
5. 12

Ans – Answer: C
Total number of balls = 15
Number of green balls =x
Number of red balls = 15 – x
xC₁ / 15C₁ = 0.4
x = 6
Number of red balls = 15 – 6 = 9

Q5. A bag contains 5 yellow, 3 blue and 4 white shirts. 2 shirts are taken out randomly. What is the probability that one shirt is yellow and other shirt is blue?

1. 6/23
2. 3/22
3. 5/22
4. 2/11
5. 4/33

Ans – Answer: C

Total number of shirts = 5 + 3 + 4 = 12
No. of ways of drawing 2 shirts = 12C₂ = (12*11)/2 = 66
No. of ways of drawing 1 yellow and 1 blue shirt = (5C₁*3C₁) = 5*3 = 15
Probability = 15/66 = 5/22

Q6. Movie Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

1. 1/2
2. 3/5
3. 9/20
4. 8/15
5. None

Answer: C) 9/20

Here, S = {1, 2, 3, 4, …., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20.

Q7. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

1. 2/7
2. 5/7
3. 1/5
4. 1/2
5. None

Answer: A) 2/7

Total number of outcomes possible, n(S) = 10 + 25 = 35
Total number of prizes, n(E) = 10
P(E)=n(E)n(S)=10/35=2/7

Q8. What is the probability of getting a sum 9 from two throws of a dice?

1. 1/2
2. 3/4
3. 1/9
4. 2/9
5. None

Answer: C) 1/9

In two throws of a die, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =n(E)/n(S)=4/36=1/9.

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