Class 10 – Probability – Important Questions

Probability – Important Questions

1. A box contains 90 discs, numbered from 1 to 90. If 1 disc is drawn at random from the box, the probability that it bears a prime number less than 23, is :
   1. 7/90
   2. 10/90
   3. 4/45
   4. 9/89
2. What is the sum of the probabilities of all the elementary events of an experiment ?
3. One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will
   (i) be an ace,
   (ii) not be an ace.
4. Two dice are thrown at the same time. Find the probability of getting
   (i) the same number on both dice.
   (ii) different numbers on both dice
5. Two players, Sangeeta and Reshma, play a tennis match. It is known
   that the probability of Sangeeta winning the match is 0.62. What is the probability of Reshma winning the match?
6. Savita and Hamida are friends. What is the probability that both will
   have
   (i) different birthdays?
   (ii) the same birthday? (ignoring a leap year).
7. What is the probability of 53 Sundays in a year ? (ignoring a leap year).
8. Harpreet tosses two different coins simultaneously. What is the probability that she gets at least one head?
9. Two friends were born in the year 2000. What is the probability that they have the same birthday?
10. The king, queen and jack of diamonds are removed from a pack of 52 cards and then the pack is well-shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of        
    (i) diamonds        
    (ii) a Jack
11. in a game of chance there is spinning of an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and there are equally likely outcomes. What is the probability that it will point at        
    (i) 7?                        
    (ii) an odd number?        
    (iii) a number less than 9?
12. A bag contains 12 balls out of which x are white.
    (i) If one ball is drawn at random, what is the probability that it will be a white ball?
    (ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in case (i). Find x.
13. A bag contains tickets, numbered 11, 12, 13, …., 30. A ticket is taken out from the bag at random. Find the probability that the number on the drawn ticket        
    (i) is a multiple of 7        
    (ii) is greater than 15 and a multiple of 5.
14. Five cards—the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.
    (i) What is the probability that the card is the queen?
    (ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?
15. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.
16. A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is
    (i) extremely patient.
    (ii) extremely kind or honest.
    Which of the above values you prefer more ?