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# Most Common Probability Aptitude Questions & Answers in 2023 [For Freshers]

Last updated:
10th Mar, 2021
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6 Mins    View All  Probability refers to the quantitative measure of the likelihood of an event occurring. It is either expressed in percentages or proportions in the range 0% to 100% or 0 to 1 respectively.

Here are basic formulas and concepts that help compute the probability of an event:

 Probability Range 0 = P(A) = 1 Rule of Complementary Events P(AC) + P(A) = 1 Rule of Addition (A or B) = P(A) + P(B) – P(AnB) Disjoint Events P(AnB) = 0 Conditional Probability P(A | B) = P(AnB) / P(B) Bayes Formula P(A | B) = P(B | A) × P(A) / P(B) Independent Events P(AnB) = P(A) × P(B) Cumulative Distribution Function FX(x) = P(X = x)

We also use concepts of permutations and combinations to find the probability of an event.

Now, let’s look at some example probability aptitude questions and answers so you know how different types of questions in probability are approached.

## Probability Aptitude Questions and Answers

Question 1: Two brothers X and Y appeared for an exam. Let A be the event that X is selected and B is the event that Y is selected.

The probability of A is 1/8 and that of B is 1/7. Find the probability that both of them are selected.

A) 1/63

B) 2/65

C) 1/56

D) 9/76

Solution:

Option C (1/56) is the right answer.

Given, A is the event that X is selected and B is the event that Y is selected.

P(A)=1/8, P(B)=1/7

If C be the event that both are selected, then

P(C)=P(A)×P(B) {A and B are independent events}

= (1/8)×(1/7)

= 1/56

Question 2: A person begins with 128 rupees and makes 6 bets, winning three times and losing three times, in random order. Both chances of winning and losing are equal. If each wager is for half the money remaining at the time of the bet, then the final result is:

A)  gain of Rs 54

B) a loss of Rs 74

C) neither gain nor a loss

D) a gain or a loss depending upon the order in which the wins and losses occur

Solution:

Option B is the right answer.

Each win implies multiplying the amount by 1.5 and loss implies multiplying the amount by 0.5. Therefore, we will multiple 1.5 three times with the initial amount as well as multiply 0.5 three times.

The resultant amount in each case will be:

⇒ 128(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 54

Hence the final result is:

⇒ 128 − 54 = 74

I.e., a loss of Rs 74

Question 3: A box contains 2 blue, 3 red, and 2 green balls. If a ball is drawn randomly, what is the probability that none of the balls is green?

A) 10/12

B) 10/21

C) 10/13

D) 10/31

Solution

Option B is the right answer.

Number of balls in the box = (2+3+2) = 7

If S is the sample space.

Then, n(S) is the total number of ways you can draw 2 balls out of 7

⇒ 7C2 = (7×6)/(2×1) = 21

Let E be the event of drawing 2 balls out of the box, which isn’t green.

⇒ n(E) = number of ways you can draw 2 balls out of the remaining (2+3) balls in the box

= 5C2

⇒ (5×4)/2 = 10

Therefore, P(E) = n(E)/n(S) = 10/21

Question 4: If a bag contains 23 toys having numbers 1 to 23 and two toys are drawn at random one after another (without replacement of the first toy), what is the probability that both toys will have even numbers?

A) 5/21

B) 9/42

C) 11/42

D) 5/23

Solution:

Option D is the right answer

There are 11 even numbers between 1 and 23. Therefore, the probability that the first toy shows have an even number is

= 11/23

Since the first toy is not replaced, there are 10 even number of toys left in the bag is a total of 22 toys.

Hence, the probability that the second toy is numbered even is,

= 10/22

Resultant probability =11/23)×(10/22)

=5/23

Question 5: X speaks the truth in 75% of cases and Y speaks the truth in 80% of cases. What is the percentage of cases that are likely to contradict each other while narrating the same event?

A) 45%

B) 5%

C) 35%

D) 22.5%

Solution:

Option C is the right answer.

There can be two cases of X and Y contradicting each other,

Case I: X speaks the truth and Y does not.

Case II: X does not speak the truth and Y speaks the truth.

⇒ (3/4×1/5) + (1/4×4/5) = 3/20 + 4/20 = 7/20

Therefore, the percentage is 35%.

Question 6: Given a set of numbers {1, 2, 3, …., 125}. If a number is chosen at random from the above set, what is the probability that the chosen number will be a perfect cube?

A) 1/2

B) 1/25

C) 4/13

D) 1/10

Solution

Option B is the right answer

There are five perfect cubes between 1 and 100 ⇒ 1, 8, 27, 64 and 125.

Therefore, the probability of picking a perfect cube from the given sample space is

= 5/125

= 1/25

Also Read: Interview Tips to Stand out

## Conclusion

Acing a probability aptitude test requires practice and familiarity with the kind of questions commonly asked. Go through the basic probability formulas and concepts and practice as much as you can to feel confident about solving probability problems easily. Good luck!

The big challenge in life is to convert the barrier into an opportunity.  ‘Now’ is always the best time to upskill yourself with latest technologies. Checkout upGrad’s top courses in Data ScienceMachine LearningDigital Marketing, MBA from LBSFull Stack Development.  #### Nitin Gurmukhani

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1What are the real-life uses of probability?

Probability is the study of events that may or may not occur. Most of the time, we use it without even realising it. In everyday life, we don't solve actual probability issues. Instead, we use subjective probability to decide on a course of action or make any decision. To forecast the weather, meteorologists employ a specialised instrument and approach. They examine every other historical database of days with identical temperature, moisture, pressure parameters, etc. Many political analysts employ probability-based strategies to forecast election results. Probability aids in the evaluation of the appropriate insurance plan for you and your family. One of the most fascinating instances of probability is winning or losing a lottery.

2What is an aptitude test?

An aptitude test can be defined as a test that determines a person's ability or proclivity to excel in a certain activity. According to aptitude tests, individuals are said to have intrinsic talents and limitations and a natural inclination toward success or failure in different areas based on their innate qualities. Most individuals take an aptitude test to see what sorts of jobs are suitable for their abilities and interests. High school students usually take an aptitude test to decide what college degree to pursue or which college is the best option for them. The human resources departments of some firms also employ career evaluation exams to learn about a candidate's skills and shortcomings.

3How does the medical field make use of probability?

Part of medical decision-making is based on the probability of sickness. Current management recommendations for common illnesses are increasingly based on scores that employ artificial probability criteria. Doctors employ statistics and probability in a variety of situations. Probability aids them in communicating risk levels to patients. It assists them in gaining access to clinical recommendations and evidence summaries, evaluating medical marketing and promotional materials, interpreting screening test findings, and doing research. Probability theory is used to explore the relationship between exposures and the likelihood of negative health effects in epidemiology.

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