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Probability

Exercise 1

Question: 1. Complete the following statements:

(ii) The probability of an event that cannot happen is . Such an event is called.

Answer:- 0 . Impossible Event

(iii) The probability of an event that is certain to happen is . Such an event is called .

Answer:- 1, Sure Event

(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. Question: 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: All events have two possible outcomes so both outcomes 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?

Answer: Because of equal chance of both outcomes

4. Which of the following cannot be the probability of an event?

(A) 2/3 (B) –1.5 (C) 15% (D) 0.7

Answer: B cannot be a probability as it has negative value

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

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: 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? 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 10. A piggy bank contains hundred 50p coins, fifty Re 1 coins, twenty Rs 2 coins and ten Rs 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 ? 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. What is the probability that the fish taken out is a male fish? 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, and these are equally likely outcomes. What is the probability that it will point at

(i) 8 ? (iv) a number less than 9?

Answer: 1 (since all numbers are less than 9)

13. A die is thrown once. Find the probability of getting

(i) a prime 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 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? (b) a queen?

Number of favourable events = 0

P (E) = 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.

Answer: Total number of events = 132 + 12 = 144

Number of favourable events = 132 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?

Answer: Total Number of events = 20

Number of favourable events = 4 (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: Total number of events = 19

Number of favourable events = 15 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

Answer: Total number of events = 90

Number of favourable events = 90 – 9 = 81

(single digit numbers are from 1 to 9) (ii) a perfect square number

Answer: Number of favourable events can be counted by making following list of square numbers:

4, 9, 16, 25, 36, 49, 64, 81 (iii) a number divisible by 5.

Answer: The largest number divisible by 5 is 90 19. A child has a die whose six faces show the letters as given below: 20. Suppose you drop a die at random on the rectangular region shown below. 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 ? 22. 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: Possible outcomes of 3 tossing of coin

1st = HHH

2nd = HHT or HTH or THH

3rd = TTH or THT or HTT

4th = TTT

Total number of events = 8

Number of favourable events = 6 (refer to 2nd and 3rd case) 23. A die is thrown twice. What is the probability that

Answer: Possible outcomes of 2 throws of a die: Total number of events = 36

(i) 5 will not come up either time? 24. 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 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 ½

Answer: This is correct. Number of both outcomes is equal.

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