Probability Formulas & Questions for GMAT

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Probability Formulas

Everyone adores watching cricket and betting on the odds of winning and losing. Guessing what would be the probable outcome of next shot of Virat Kohli, is basically determining the probability of your win. Probability is one of the most interesting topics in the vast syllabus of competitive exams. One such esteemed exam which offers question based on probability formulas is Graduate Management Aptitude Test (GMAT) which is an essential test to qualify if one is planning to study abroad. If you are taking the GMAT 2021 examination, here is a blog with a list of probability questions to practice. 

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List of Probability Formulas 

One of the most important probability formulas is:

P(A)= Number of Favourable Outcomes / Total Number of Favourable Outcomes

Other than this one, tabulated below are some of the famous and often used Probability Formulas-

Name  Formula
Probability Range  0≤ P(A) ≤ 1
Rule of Addition  P (AuB)= P(A) + P (B)- P (A ∩ B) 
Disjoint Events P (A ∩ B)= 0
Rule of Complementary Events P(A’) + P(A)= 1
Conditional Probability  P (A | B)= P (A ∩ B)/ P(B)
Independent Events  P (A ∩ B)= P(A). P(B)
Bayes Formula P (A | B)= P (B | A). P(A)/ P(B)

Have a look at Mental Maths: Tips & Tricks to reduce your calculation time! 

List of Probability Questions 

Now that you are familiar with probability formulas, let us solve some questions to get a better hold of the formula.

  1. 60% of the balls in a bag are red and 45% of those balls are numbered. If one ball is to be picked out at random, what is the probability that the ball was taken out was a red numbered ball? 
  2. In a certain society, there are 300 female members and 100 male members. It is recorded that 20% of the female members have higher degrees whereas 40% of the male members higher degrees. If 1 member is chosen out of the total members of a society, what is the probability that the member has a higher degree or is female?
  3. Rohit flipped a coin, the probability that the coin will land as heads is 1/2. He flips the coin 5 times, what is the probability that the coin will land as heads up only in the first 3 attempts and not on the last 2 attempts of flipping?
  4. A couple has 3 males children and 5 female children. If a football team of children is to be randomly selected, what is the probability of having only 2 female children in the team?
  5. Simran had drawn 4 birthday cards for 4 different students of her with different addresses. To post each birthday card she had bought 4 separate envelopes. If she puts 4 letters into 4 envelopes randomly, what is the probability only 1 letter will be put into the envelope with the correct address. 

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  1. Tanya is expected to speak truth 2 out of the 3 times. When a dice was rolled and she reported that the number obtained is 4. Find out the probability that the number obtained is actually 4.
  2. Basket 1 contains 4 black balls and 6 red balls, as well as the basket 2, contains 4 black balls and 3 red balls. If one ball was picked at the random from one of the baskets turns out to be black. Find the probability that it was from basket 2.
  3. There is a treasure box A which has 100 gold coins whereas the treasure box B has 50 silver and 50 gold coins. You are asked to pick a coin randomly and a gold coin comes out. What is the probability that picked out coin belongs to treasure box A?
  4. In my bag, there are 8 fair coins which have Tails on one side and Head on the other. Along with this, there is 1 erroneous coin which has heads on both sides. My brother select a coin randomly and flips it 4 times. Doing so he receives heads all four times. What is the probability of getting heads again if he flips the same coin one more time?
  5. As per the general notion, the probability that it will rain on Tuesday is 25%. Also, if it rains on Saturday, the probability that it will rain on Thursday as well, is 50%. If it does not rain on Tuesday, the probability that it will rain on Thursday is 25%. Let us assume that it rained on Thursday, what is the probability that it will rain on Tuesday?

The likelihood of an event occurring is calculated using the probability formula. Remember that probability is the possibility of an event occurring. One of the first questions we ask when considering a random experiment is: What are the chances that a particular outcome would occur? A prediction’s likelihood is its probability.


What are the formulas of probability?

P(A) = n(A)/n(S)
P(A) is the probability of an event “A”
n(A) is the number of favourable outcomes.
n(S) is the total number of events in the sample space.

What is the probability simple formula?

Probability = A formula for estimating the likelihood that a particular outcome will occur in a given event. In this instance the likelihood that a coin will land on heads. Probability of an event = (number of possible outcomes) / (total number of outcomes)

What is the rule of Probability:

P() = 0 *An impossible event has the smallest conceivable probability (null set ). 2. P(S) = 1 * The occurrence having the highest probability is one where S is the sample space.

Read Vedic Maths Tricks to Reduce your Calculation Time!

These probability formulas and questions will definitely help you in fetching a great GMAT score. Reach out to Leverage Edu and join our online preparatory classes for the upcoming GMAT exam!

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