PROBABILITY 215
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 a50 p coin ? (ii) will not be

a5 coin?

11. Gopi buys a fish from a shop for his aquarium. The
shopkeeper takes out one fish at random from a ra
tank containing 5 male fish and 8 female fish (see (Nap, 85
Fig. 14.4). What is the probability that the fish taken i was

tisamalefish? ° (Ves aecOy

out is a male fish? ys 3

12. A game of chance consists of spinning an arrow
which comes to rest pointing at one of the numbers Fig. 14.4
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 °
Oe , fi yr)

@) 8?

(ii) an odd number? , ° (6 / \ 3
(ui) a number greater than 2? 5 : : .

+ 9 * °

(iv) anumber less than 9? . . Fig. 14.5

13. A die is thrown once. Find the probability of getting
(i) a prime number; (ii) anumber 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) aking of red colour - (ii) a face card (iit) 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?
(i) 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?

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.

17. @ 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?

(tt) 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) anumber divisible by 5.

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216 MATHEMATICS

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

[>|
The die is thrown once. What is the probability of getting (ij)A? (i) D?
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 1m?
3m
OO] "
Fig. 14.6 - OO

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 .

(@) She will buy it ? , : .
(i) She will not buy it? .
22. Refer to Example 13. (i) Complete the following table:
Event:
'Sum on2dice' | 2 3 4 5 7 10} | 2
Probabili 4+ = 1
robability 36 36 36
(i) A student argues that 'there are 11 possible outcomes 2, 3, 4,5, 6, 7, 8,9, 10, 11 and
os ]
12. Therefore, each of them has a probability Th Do you agree with this argument?
Justify your answer.

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? Gi) 5 will come up at least once?
[Hint : Throwing a die twice and throwing two dice simultaneously are treated as the
same experiment]
* Not from the examination point of view.
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PROBABILITY 217
25. Which of the following arguments are correct and which are not correct? Give reasons
for your answer.
Gi) 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
1
probability is 3
(i) Ifa die is thrown, there are two possible outcomes-an odd number or an even
1
number. Therefore, the probability of getting an odd number is 5°
14.2 Summary
In this chapter, you have studied the following points :
1. The theoretical (classical) probability of an event E, written as P(E), is defined as
PE) Number of outcomes favourable to E
~ Number of all possible outcomes of the experiment
where we assume that the outcomes of the experiment are equally likely.
2. The probability of a sure event (or certain event) is l.
3. The probability of an impossible eventis 0. -
4, The probability of an event E is a number P(E) such that
fo O<PE)<1 ©
5. An event having only one outcome is called an elementary event. The sum of the
probabilities of all the elementary events of an experiment is 1.
6. For any event E, P (E) + P(B) = 1, where £ stands for 'not E'. E and £ are called
complementary events. ,
_ A NOTE TO THE READER
The experimental or empirical probability of an event is based on
what has actually happened while the theoretical probability of the
event attempts to predict what will happen on the basis of certain
assumptions. As the number of trials in an experiment, go on
increasing we may expect the experimental and theoretical
probabilities to be nearly the same.
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