Class 10 › Mathematics Probability Class 10 Mathematics · Chapter 14
Practice all → Summary Questions & answers Practise this chapter → View all Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). This chapter develops the theoretical (classical) definition: the probability of an event equals the number of favourable outcomes divided by the total number of equally likely outcomes. It applies this to everyday experiments such as tossing coins, rolling dice and drawing cards, and uses the fact that the probabilities of an event and its complement add up to 1. Probability provides a precise language for reasoning about chance and uncertainty.
Probability of an event
\(P(E) = \dfrac{\text{favourable outcomes}}{\text{total outcomes}}\).
Sure/impossible event
Probability 1 (certain) or 0 (impossible).
Complementary event
\(P(\text{not }E) = 1 - P(E)\).
Equally likely outcomes
Outcomes that each have the same chance of occurring.
Q1 What is the probability of a sure event and an impossible event? Answer Q2 If \(P(E) = 0.3\), what is \(P(\text{not }E)\)? Answer Q3 Write the formula for the theoretical probability of an event E. Answer Q4 What is the probability of a sure event and of an impossible event? Answer Q5 What is the range of the probability of any event? Answer Q6 What are complementary events, and how are their probabilities related? Answer Q7 A die is thrown once. What is the probability of getting an even number? Answer Q8 A card is drawn from a well-shuffled pack of 52. What is the probability that it is a king? Answer Q9 Two coins are tossed together. What is the probability of getting two heads? Answer Q10 If the probability of an event is 0.7, what is the probability of its not happening? Answer Q1 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 ______. Answer Q2 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 answer a true-false question. The answer is right or wrong.
(iv) A baby is born. It is a boy or a girl. Answer Q3 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? Answer Q4 4. Which of the following cannot be the probability of an event?
(A) \(\frac{2}{3}\) (B) \(-1.5\) (C) \(15\%\) (D) \(0.7\) Answer Q5 5. If \(P(E)=0.05\), what is the probability of ‘not E’? Answer Q6 6. A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out
(i) an orange flavoured candy?
(ii) a lemon flavoured candy? Answer Q7 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? Answer Q8 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? Answer Q9 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? Answer Q10 10. A piggy bank contains hundred \(50\text{p}\) coins, fifty \(\text{₹}1\) coins, twenty \(\text{₹}2\) coins and ten \(\text{₹}5\) 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 \(50\text{ p}\) coin ? (ii) will not be a \(\text{₹}5\) coin? Answer Q11 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. 14.4). What is the probability that the fish taken out is a male fish? Answer Q12 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. 14.5 ), 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 \(9\)? Answer Q13 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. Answer Q14 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 Answer Q15 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? Answer Q16 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. Answer Q17 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 ? Answer Q18 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 \(5\). Answer Q19 19. A child has a die whose six faces show the letters as given below:
A B C D E A
The die is thrown once. What is the probability of getting (i) A? (ii) D? Answer Q20 20*. Suppose you drop a die at random on the rectangular region shown in Fig. 14.6. What is the probability that it will land inside the circle with diameter \(1\text{m}\)? Answer Q21 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 ? Answer Q22 22. Refer to Example 13. (i) Complete the following table:
Event :
‘Sum on \(2\) dice’ \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\) \(12\)
Probability \(\frac{1}{36}\) ______ ______ ______ ______ ______ \(\frac{5}{36}\) ______ ______ ______ \(\frac{1}{36}\)
(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 \(\frac{1}{11}\). Do you agree with this argument? Justify your answer. Answer Q23 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. Answer Q24 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] Answer Q25 25. Which of the following arguments are correct and which are not correct? Give reasons for your answer.
(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 \(\frac{1}{3}\).
(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 \(\frac{1}{2}\). Answer
The theoretical probability of an event E is:
A (total outcomes)/(favourable outcomes) B always 1/2 C favourable outcomes × total outcomes D (number of favourable outcomes)/(total number of outcomes)
Flashcards & interactive practice 
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