# NCERT Solution for Class 10 Mathematics Chapter 15 Probability

 Chapter Name NCERT Solution for Class 10 Maths Chapter 15 Probability Topics Covered Short Revision for the ChapterNCERT Exercise Solution Related Study NCERT Solution for Class 10 MathsNCERT Revision Notes for Class 10 MathsImportant Questions for Class 10 MathsMCQ for Class 10 MathsNCERT Exemplar Questions For Class 10 Maths

## Short Revision for Probability

1. P(E) = (number of outcomes favourable to E)/(number of all possible outcomes).
2. An outcome of a random experiment is called an elementary event.
3. The sum of the probabilities of all the elementary events of an experiment is 1.
4. The probability of an impossible event is 0.
5. The probability of a sure event is 1.
6. For any event E,
0≤ P(E) ≤ 1.
7. Probability of an event cannot be negative.
8. If E and E represent respectively occuring and not occuring an event, then,
P(E) + P(E) = 1.
9. E and E are called complementary events.

### NCERT Exercise Solutions

#### Exercise: 15.1

1. Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ = ___________.
(ii) The probability of an event that cannot happen is __________. Such an event is called ________.
(iii) The probability of an event that is certain to happen is _________. Such an event is called _________.
(iv) The sum of the probabilities of all the elementary events of an experiment is __________.
(v) The probability of an event is greater than or equal to and less than or equal to __________.

Solution

(i) 1
(ii) 0, impossible event
(iii) 1, sure event
(iv) 1
(v) 0, 1.

2. Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.
(iii) A trial is made to Solution: a true-false question. The Solution: is right or wrong.
(iv) A baby is born. It is a boy or a girl.

Solution

In case (i) and (ii)  events can be favourable to particular event, so not equally likely, whereas in (iii) and (iv)  events are equally likely.

3. Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

Solution

Because, both the events 'Head' or 'Tail' are equally likely to occur.

4. Which of the following cannot be the probability of an event?
(A) 2/3

(B) -1.5

(C) 15%

(D) 0.7

Solution

(B), as probability of an event cannot be negative.

5. If P(E) = 0.05, what is the probability of ‘not E’?

Solution

P(not E) = 1 - P(E) = 1 - 0.05 = 0.95.

6. A bag contains lemon flavored candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out
(i) an orange flavored candy?
(ii) a lemon flavored candy?

Solution

(i) As there are only lemon flavoured candies, therefore, getting an orange flavoured candy is an impossible event. Hence probability is 0.
(ii) Lemon flavoured candy is a sure event, hence probability  is 1.

7. It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

Solution

P(two students having the same birthday)
= 1 - P (two students not having the same birthday)
= 1 - 0.992 = 0.008.

8. 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

Total balls ( 3 red  + 5 black) = 8 balls.
(i) Probability of a red ball = 3/8
(ii) Probability of  not a red ball = 1 - P(red ball )
= 1 - 3/8 = 5/8 .

9. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be
(i) red?
(ii) white?
(iii) not green?

10. A piggy bank contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹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
(i) will be a 50 p coin?
(ii) will not be a ₹5 coin?

11. Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see Fig. 15.4). What is the probability that the fish taken out is a male fish?

Solution
Total number of fish in the tank = (5 male + 8 female) fish = 13 fish
∴ Probability of male fish = 5/13.

12. A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see Fig. 15.5), and these are equally likely outcomes. What is the probability that it will point at
(i) 8?
(ii) an odd number?
(iii) a number greater than 2?
(iv) a number less than 9?

13. A die is thrown once. Find the probability of getting
(i) a prime number;
(ii) a number lying between 2 and 6;
(iii) an odd number.

14. 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 red face card
(iv) the jack of hearts
(v) a spade
(vi) the queen of diamonds

15. 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?

Solution

(i) Total cards = 5
Favourable for queen  = 1.
Therefore, probability is 1/5.
(ii) (a) Four possible cases and one is favourable, so, probability is 1/4.
(b) None is favourable. Therefore, probability is 0.

16. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

Solution

Total pens are 144, (12 defective + 132 good ones).
favourable cases for good pen are 132.
∴ Probability of drawing a good pen = 132/144 = 11/12.

17. (i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

18. 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
(i) a two-digit number
(ii) a perfect square number
(iii) a number divisible by 5.

19. A child has a die whose six faces show the letters as given below:

The die is thrown once. What is the probability of getting
(i) A?
(ii) D?

Solution

(i) Here, A is shown on two faces so favourable cases = 2
∴ (ii) Favourable case is only 1. So, probability of getting D = 1/6.

20. Suppose you drop a die at random on the rectangular region shown in Fig. 15.6. What is the probability that it will land inside the circle with diameter 1m?

21. A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
(i) She will buy it?
(ii) She will not buy it?

Solution

Total ball pens are 144, defective ball pens are 20, non - defective ball pens are 124.
(i) Probability that Nuri buys these pens
= P(non - defective pen) = 124/144 = 31/36.
(ii) Probability that Nuri does not buy it
= P(defective pen) = 20/144 = 5/36.

22. Refer to Example 13. (i) Complete the following table:

(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability 1/11. Do you agree with this argument? Justify your Solution: .

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

24. A die is thrown twice. What is the probability that
(i) 5 will not come up either time?
(ii) 5 will come up at least once?
[Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]

25. Which of the following arguments are correct and which are not correct? Give reasons for your Solution:.
(i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3
(ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is 1/2

#### Exercise: 15.2

1. Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on
(i) the same day?
(ii) consecutive days?
(iii) different days?

2. A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:

What is the probability that the total score is
(i) even?
(ii) 6?
(iii) at least 6?

3. 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.

Solution

Let number of blue balls be x. Red balls are 5.
Total balls = 5 +x.
Probability of blue ball = 2 × probability of red ball

∴ Total blue balls are 10.

4. A box contains 12 balls out of which x are black. If one ball is drawn at random from the
box, what is the probability that it will be a black ball?
If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x

5. A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at
random from the jar, the probability that it is green is ⅔. Find the number of blue balls in the jar.