# 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 MATHEMATICSProbability – Chapter 15**

- 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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.