Cluster · Probability and Permutations

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Clusters / #1120
umbrella score 0.73

Permutations Combinations and Probability
Questions
200
Umbrella sub-concepts
Combinations and counting Permutations of letters with constraints Probability (dice, coins) combinations and committee selection grouping arrangements permutations of words with repeated letters probability calculations with dice
Questions in this cluster
200 total
Question Category Subtype Difficulty

There are a total of 18 balls in a bag. Out of them, 6 are red, 4 are green, and 8 are blue. If Vishal picks three balls randomly from the bag, then what will be the probability that all three balls are not of the same color?

pipeline-1297048
mp_police intermediate

In a family 40% of the members drive cars, 25% ride bikes, and 10% drive both. If a member is selected at random, what is the probability that they drive a car or a bike?

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mp_police intermediate

The odds against an event is 7 : 4 and the odds in favour of another event is 8 : 5. If both the events are independent, then the probability that at least one of the event will happen is:

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mp_police intermediate

Two dices are rolled simultaneously. What is the probability that both the dices show same number?

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mp_police intermediate

A box contains 10 identical electronic components, of which 4 are defective. If 3 components are selected at random from the box in succession without replacing the units already drawn, what is the probability that two of the selected components are defective?

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mp_police intermediate

A packet contains 12 tablets out of which 5 are blue in colour and rest of them are red in colour. If 2 tablets are picked from the packet, then what is the probability that both of them are of the same colour?

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mp_police intermediate

If we select 3 persons randomly from a group consisting of 4 men, 3 women, and 2 boys, then the probability that 2 men are selected is:

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mp_police intermediate

A pair of fair dice is thrown. What is the probability that the sum of the numbers on both dice is 5?

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mp_police dice_cube intermediate

In a bag, there are 3 green balls, 5 white balls, and 8 orange balls. What is the minimum number of balls that must be drawn such that there are at least four balls of the same color?

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bihar_police intermediate

In how many ways can a group of 6 boys and 2 girls be made out of the total of 7 boys and 3 girls?

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bihar_police intermediate

The probability that a card drawn from a pack of 52 cards will be an spade or king being to:

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bihar_police intermediate

7 boys and 5 men are to be seated in a row on 12 chairs in such a way that all the 5 men always sit together. In how many different ways can it be done?

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bihar_police intermediate

A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is

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bihar_police dice_cube intermediate

Three fair coins are tossed simultaneously. What is the probability of getting at least 1 head?

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bihar_police intermediate

A fair coin is tossed independently four times. The probability of the event ‘the number of times heads show up is more than the number of times tails show up’ is

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bihar_police intermediate

What is the probability that result of the dice rolled is a prime number?

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bihar_police dice_cube intermediate

In a well-shuffled pack of cards, a card is chosen. What is the probability that it is either a face card or a diamond?

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bihar_police intermediate

What is the number of ways in which 5 boys and 5 girls can be seated in a circle such that no girls are together?

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bihar_police intermediate

In how many ways can 3 red balls, 2 green balls, and a white ball be arranged in a line?

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bihar_police intermediate

A bag contains 3 red, 5 white and 4 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

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bihar_police intermediate

In how many ways a committee, consisting of 8 men and 6 women can be formed from 12 men and 12 women?

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bihar_police intermediate

In a well-shuffled pack of cards, a card is chosen. What is the probability that it is either a face card or a diamond?

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bihar_police intermediate

From a pack of playing cards, all the red coloured face cards has been removed. A card is then drawn from the remaining cards. What is the probability that the card drawn is a king? 

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up_police intermediate

Sumit can't remember the last four numbers of his brother's phone number when he dials it. He dialed at random, remembering only that these digits were different. What is the probability that the number Sumit dialed was the right one?

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up_police intermediate

A person can hit a target 5 times out of 8 shots. If he fires 10 shots, what is the probability that he will hit the target twice?

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up_police intermediate

What is the probability of the vowels coming in even places if the letters of the word 'MOBILE' have been arranged in every possible way?

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up_police intermediate

Two cards are drawn from the pack of 52 cards. What is the probability of getting either an ace of diamond or a queen of spade?

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up_police intermediate

What is the probability of getting a co-prime when two dices are thrown?

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up_police intermediate

A letter of the English alphabet is chosen at random. The probability of getting a vowel is:

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up_police intermediate

If \(P(A \cup B) = \frac{5}{9}, P(\bar{A}\cup \bar{B})=\frac{13}{27}, P(A) = \frac{11}{18}\), then the odds against event B are:

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up_police intermediate

What is the probability of drawing an ace from a pack of 52 cards?

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up_police intermediate

In a lottery of 10 tickets numbered 11 to 20, two tickets are drawn simultaneously. What is the probability that both the tickets drawn have prime numbers?

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up_police intermediate

A box contains 6 white balls and 7 black balls. Two balls are drawn at random. What is the probability that both of them are of different colours?

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up_police intermediate

A bag contains 5 red, 6 black, 4 green, and 3 white marbles. If 2 marbles are drawn randomly from the bag, find the probability that both are white marbles.

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up_police intermediate

There are 4 red pens and 7 green pens. If one randomly draws a pen what is the probability of getting a red pen?

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up_police intermediate

If Sandeep rolled two dices at the same time then what is the probability of getting a sum of 9 or more than 9 on the dices?

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up_police intermediate

Two numbers are selected from the set of first six natural numbers. What is the probability that their difference is 1?

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up_police intermediate

If a dice is defective such that it has 2 five instead of one so what is the probability of getting a 4?

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banking dice_cube intermediate

How many different ways can the letters of the word 'SOLUTION' be arranged so that all the vowels are always together?

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delhi_police intermediate

In how many ways can the letters of the word "ARRANGEMENT" be arranged?

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delhi_police intermediate

In how many ways can the letters of the word "SUSTAIN" be arranged?

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delhi_police intermediate

Find the number of ways of arranging the letters of the word "BANANA".

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delhi_police intermediate

Find the number of ways of arranging the letters of the word "REFERENCE".

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delhi_police intermediate

How many different ways can the letters of the word 'CHEMISTRY' be arranged so that all the vowels are always together?

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delhi_police intermediate

How many different words can be formed with the letters of the word 'MOBILES' such that each word begins with O and ends with S?

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delhi_police intermediate

In how many ways can the letters of the word "HOPELESS" be arranged?

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delhi_police intermediate

Find the number of ways of arranging the letters of the word "ACCOMMODATE".

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delhi_police intermediate

In how many ways can the letters of the word "SPONTANEOUS" be arranged?

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delhi_police intermediate

Find the probability of getting a sum of at least 8 while throwing 2 dice if neither of the two dice shows a number less than 4.

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railways dice_cube intermediate

What is the probability of getting a co-prime when two dices are thrown?

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railways intermediate
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