Probability – Class 10

Chapter 15 of NCERT/CBSE Class 10 Mathematics is about Probability. Here in this lesson you can find practice problems for this chapter.

IMPORTANT QUESTIONS FOR CBSE CLASS 10 MATHEMATICS
Probability – Chapter 15

1. Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail?
   Solution:
   The number of possible outcomes is Head and Tail.
   Let E be the event getting a head. The number of outcomes favorable to E is one. Therefore, P (E) = P (Head) = ½.
   Similarly, if F is the event getting a tail then P (F) = P (Tail) = ½.
2. A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a) a vowel, b) a consonant.
   Solution:
   Number of vowels in English alphabet is 5 and consonant is 21.
   Therefore, probability of getting a vowel is 5/26 and consonant is 21/26.
3. One card id 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.
   Solution:
   i) There are 4 aces in a deck. Let E be the event the card is an ace.
   He number of outcomes favorable to E = 4
   The number of possible outcomes = 52
   Therefore, P (E) = 4/52 = 1/ 13.
   ii)Let be the event card drawn is not an ace.
   The number of outcomes favorable to the event F = 52 – 4 = 48
   The number of possible outcomes = 52
   Therefore, P (F) = 48/52 = 12/13.
4. Find the probability of getting a red face card from a well shuffled pack of 52 cards.
   Solution:
   The number of possible outcomes = 52
   Number of red face cards = 6
   Probability of getting a red face card = 6/52 = 3/26.
5. A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the card drawn is neither an ace nor a queen?
   Solution:
   Number of ace = 4
   Number of queen = 4
   Therefore, P (neither ace nor queen) = 44/52 = 11/13.
6. A die is thrown once. Find the probability of getting:
   i) a prime number
   ii) a composite number
   Solution:
   i) Total outcomes = 6
   Prime numbers are 2, 3 and 5.
   P (a prime number) = Number of favorable outcomes/total number of outcomes.
   = 3/6
   = ½.
   Composite numbers are 4 and 6.
   P (a composite number) = 2/6 = 1/3.
7. A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be
   i) white
   ii) blue
   iii) red.
   Solution:
   The number of possible outcomes = 3 + 2 + 4 = 9
   Let W denote the event ‘the marble is white’, B denote the event ‘the marble is blue’ and R denote the event ‘marble is red’
   i) The number of outcomes favorable to the event W = 2
   So P (W) = 2/9
   ii) P (B) = 3/9
   iii) P(R) = 4/9.
8. A card is drawn from a well shuffled pack of 52 playing cards. What is the probability that the card drawn is
   i) a jack of hearts
   ii) a red face card
   Solution:
   i) P (a jack of hearts) = 1/52
   ii) P (a red face card) = 6/52 = 3/26.
9. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is
   i) red
   ii) not red
   Solution:
   Number of red balls = 3
   Number of black balls = 5
   Total number of balls = 3 + 5 = 8
   i) P (red balls) = 3/8
   ii) P (not red) = 5/8.
10. One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting
    i) a king of red colour
    ii) a face card
    iii) a spade
    iv) the queen of diamonds
    Solution:
    i) P (a king of red colour) = 2/52 = 1/26.
    ii) P (a face card) = 12/52 = 3/13.
    iii) P (a spade) = 13/52 = ¼
    iv) P ( the queen of diamonds) = 1/52.