Probability Practice Questions

A collection of quantitative reasoning questions that typically appear on Probability in MBA entrance exams such as TANCET, GMAT, and CAT. This topic is considered a tough topic. The aptitude section of these tests include the following concepts: computing probability of events involving rolling dice, tossing coins, picking cards from a pack of cards, selecting numbers, mutually exclusive events, independent events and more.

1. What is the probability of getting at least one six in a single throw of three unbiased dice?

   1. \\frac{1}{6}\\)
   2. \\frac{125}{216}\\)
   3. \\frac{1}{36}\\)
   4. \\frac{81}{216}\\)
   5. \\frac{91}{216}\\)

   Concept: Rolling Dice

   Choice (5)The probability of getting at least one six in a single throw of 3 unbiased coins is 91/216 Correct answer Explanatory Answer Medium

2. What is the probability that a two digit number selected at random will be a multiple of '3' and not a multiple of '5'?s

   1. \\frac{2}{15}\\)
   2. \\frac{4}{15}\\)
   3. \\frac{1}{15}\\)
   4. \\frac{4}{90}\\)

   Concept: Number sequences

   Choice (2)The probability that the two digit number selected will be a multiple of 3 and not a multiple of 5 is 4/15 Correct answer Explanatory Answer Medium

3. A man bets on number 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the number 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes? (Roulette has numbers 1 to 36)

   1. 16; 22 : 14
   2. 12; 72 : 14
   3. 12; 7 : 1
   4. Either; 35 : 1

   Concept: Independent Events

   Choice (4)Either; 35 : 1 Correct answer Explanatory Answer Medium

4. Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?

   1. \\frac{1}{18}\\)
   2. \\frac{64}{4032}\\)
   3. \\frac{63}{64}\\)
   4. \\frac{1}{9}\\)

   Concept: Chess Board

   Choice (1)The probability that the two chosen squares have a common side is 1/18 Correct answer Explanatory Answer Hard

5. When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11?

   1. \\frac{5}{6}\\)
   2. \\frac{11}{12}\\)
   3. \\frac{1}{6}\\)
   4. \\frac{1}{12}\\)

   Concept: Rolling Dice

   Choice (2)The probability that the sum if less than 11 is 11/12 Correct answer Explanatory Answer Easy

6. When 4 dice are rolled simultaneously, what is the probability that the same number appears on all of them?

   1. \\frac{1}{36}\\)
   2. \\frac{1}{1296}\\)
   3. \\frac{1}{216}\\)
   4. \\frac{1}{5}\\)

   Concept: Rolling Dice

   Choice (3)The probability that the same number appears on all 4 dice is 1/216 Correct answer Explanatory Answer Easy

7. An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?

   1. 0
   2. \\left[\frac{2}{3} \right]^4\\)
   3. \\ 5 * \left[\frac{2}{3} \right]^4 * \left[\frac{1}{3} \right] \\)
   4. \\left[\frac{2}{3} \right]^4 * \left[\frac{1}{3}\right]\\)

   Concept: Independent trials

   Choice (3)5 * {2/3}^4 * {1/3} Correct answer Explanatory Answer Medium

8. An anti aircraft gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy aircraft will bring the aircraft down?

   1. 0.084
   2. 0.916
   3. 0.036
   4. 0.964

   Concept: Complimentary events

   Choice (4)The probability that the aircraft will be brought down is 0.964 Correct answer Explanatory Answer Medium

9. A number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?

   1. \\frac{17}{30}\\)
   2. \\frac{2}{5}\\)
   3. \\frac{11}{30}\\)
   4. \\frac{4}{15}\\)

   Concept: Number Sequence

   Choice (2)The probability that it is a multiple of either 3 or 13 is 2/5 Correct answer Explanatory Answer Medium

10. A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?

    1. 1
    2. \\frac{1}{256}\\)
    3. \\frac{81}{256}\\)
    4. \\frac{175}{256}\\)

    Concept: Probability : Complimentary events

    Choice (4)The probability that he will hit the target is 175/256 Correct answer Explanatory Answer Medium

11. Ramesh plans to order a birthday gift for his friend from an online retailer. However, the birthday coincides with the festival season during which there is a huge demand for buying online goods and hence deliveries are often delayed. He estimates that the probability of receiving the gift, in time, from the retailers A, B, C and D would be 0.6, 0.8, 0.9 and 0.5 respectively. Playing safe, he orders from all four retailers simultaneously. What would be the probability that his friend would receive the gift in time?

    1. 0.004
    2. 0.006
    3. 0.216
    4. 0.994
    5. 0.996

    Choice EThe probability that Ramesh's friend will receive the gift is 0.996 Correct answer Explanatory Answer Video Explanation XAT 2015