# Probability Practice Questions

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A collection of questions that typically appear on Probability in MBA entrance exams such as XAT and TANCET. This topic is considered a tough topic and you could get one to three questions from this topic in XAT and one or two questions in TANCET. Concept covered includes computing probability of events involving rolling dice, tossing coins, picking cards from a pack of cards, selecting numbers based on certain criteria.

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. $\frac{91}{216}\\$ 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. $\frac{4}{90}\\$ 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
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. $\frac{1}{9}\\$
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. $\frac{1}{12}\\$
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. $\frac{1}{5}\\$
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. $\left[\frac{2}{3} \right]^4 * \left[\frac{1}{3}\right]\\$
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
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. $\frac{4}{15}\\$
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. $\frac{175}{256}\\$
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