CBSE Important Questions

PROBABILITY

Q. 1. Cards each marked with one of the numbers 4,5,6, ……..20 are placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the Probability of getting an even prime number?

Q. 2. A bag contains 5 red, 8 green and 7 white balls . one ball is drawn at random from the bag, find the Probability of getting

1. A white ball or a green ball
2. Neither a green ball nor a red ball

Q. 3. A bag contains 5 red and 4 black balls. A ball is drawn at random from the bag. What is the Probability of getting a black ball?

Q. 4. All cards of ace, jack and queen are removed from a deck of playing cards. One card is drawn at random from the remaining cards, find the v that the card drawn is

1. A face card
2. Not a face card.

Q. 5. A dice is thrown once, what is the probability of getting a prime number?

Q. 6. What is the Probability that a number selected from the numbers 1,2,3,…..15 is a multiple of 4?

Q. 7. One card is drawn from a well shuffled deck of 52 cards. Calculate the Probability that the card will a) be an ace , b) not be an ace.

Q. 8. A piggy bank contains hundred 50p coins, fifty re. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the Probability that the coin a) will  be 50p coin ? , b) will not be Rs. 5 coin?

Q. 9. The king, queen and jack of clubs are removed from the deck of 52 playing cards and then well shuffled. One card is selected from the remaining cards. Find the Probability of getting a) a king, b) a heart, c) a club d) the ‘10’ of hearts.

Q. 10. Five cards – the ten, jack, king, and ace of diamonds, are well shuffled with their face downwards. One card is then picked up at random

1. What is the Probability that the card is the queen
2. If the queen is drawn and put aside, what is the Probability that the second card picked up is i) an ace? ii) a queen?

Q. 11. A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Jimmy, a trader, will only accept the shirt which are good , but Sujatha , another trader , will only rejects the shirts which have major defects. One shirt is drawn at random from the carton. What is the Probability that

1. It is acceptable to Jimmy
2. It is acceptable to Sujatha

Q. 12. A game consists of tossing a one rupee coin 3 times and noting its outcomes each time. Hanif wins if all tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the Probability that the Hanif will lose the game.

Q. 13. Two dice are thrown simultaneously. Find the Probability that the total of the numbers on the dice is

Q. 14. Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the Probability that the sum of the two numbers appearing on the top of the dice is a) 8? b) Less than or equal 12?

Q. 15. A game of chance consists of spinning & arrow which comes to rest pointing at one of the numbers 1, 2,3,4,5,6,7,8 and these are equally likely outcomes. What is the Probability that it will point at

1. 8
2. An odd number           
3. A number greater than 2
4. A number less than 9

Q. 16. A box contains 90 discs which are numbered from 1 to 90. if one disc is drawn at  random from the box find the Probability that it bears

1. A two digit number
2. A perfect square number
3. A number divisible by 5.

Q. 17. A bag contains 35 balls out of which x are blue.

1. If one ball is drawn at random, what is the Probability that will be a blue ball?
2. If 7more blue balls are put in the bag, the Probability of drawing a blue ball will be double than it, Find x.

Q. 18. A card is drawn at random from a well shuffled pack of 52 cards. Find the Probability that the card drawn is neither a red card nor a queen.

Q. 19. A die is thrown once. What is the Probability of getting:

1. An even number
2. A multiple of 3
3. An even number or a multiple of 3
4. An even number and a multiple of 3
5. A number 3 or 4
6. An odd number
7. A number less than 5
8. A number greater than 3
9. A number between 3 and 6

  Ans. a 1/3, b) 1/3, c) 2/3, d) 1/6, e) 1/3,  f) ½, g) 2/3, h) ½, i) 1/3 )

Q. 20. Two coins are tossed simultaneously. Find the Probability of getting

1. Two heads
2. One head
3. One tail
4. At least one head
5. At most one head
6. No head

Ans. a 1/4, b) 1/2, c) 1/2, d) 3/4, e) 3/4, f) 1/4)

Q. 21. Three coins are tossed simultaneously. Find the Probability of getting:

1. All heads
2. Two heads
3. One head
4. At least two heads

Ans. a 1/8, b) 3/8, c) 3/8, d) 1/2)

Q. 22. Two dice are thrown simultaneously. Find the probability of getting:

1. An even number as the sum
2. The sum as a prime number
3. A total of at least 10
4. A doublet of even number
5. A multiple of 2 on one dice and a multiple of 3 on the other dice
6. Same number on both dice i.e. a doublet
7. A multiple of 3 as the sum

Ans. a) 1/2, b) 5/12, c) 1/6, d) 1/12, e) 11/36, f) 1 / 6, g) 1/3)

Q. 23. Find the Probability that a leap year selected at random will contain 53 Sundays (Ans. 2/7)

Q. 24. What is the Probability that a number selected from the numbers 1, 2, 3 …25 is a prime number, when each of the given number is equally likely to be selected. (Ans. 9/25)

Q. 25. A letter is chosen at random from the letters of the word “ASSASSINATION”. Find the probability that the letter chosen is a  a) vowel, b) consonant. (Ans. a) 6/13, b) 7/13)

Q. 26. A jar contains 54 marbles each of which is blue , green or white. The probability of selecting a blue marble at random from the jar is 1/3 , and the probability of selecting a green marble at random is 4/9. How many white marbles does the jar contains? ( Ans. 12)

Q. 27. A number x is selected from the numbers 1,2,3 and then a secondary number y is randomly selected from the numbers 1,4,9. What is the probability that the product xy of the two numbers will be less than 9? ( Ans. 5/9)