PROBABILITY_25 A 25B 25C_SELINA_CHAPTER 25_CLASS10_CONCISE MATHEMATICS
25A_Q
25A_Q1. A coin is tossed once. Find the probability of : (i) getting a tail. (ii) not getting a tail.
25A_Q2. A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is : (i) a black ball. (ii) a red ball. (iii) a white ball. (iv) not a red ball. (v) not a black ball.
25A_Q3. In a single throw of a die, find the probability of getting a number : (i) greater than 4. (ii) less than or equal to 4. (iii) not greater than 4.
25A_Q4. In a single throw of a die, find the probability that the number : (i) will be an even number. (ii) will not be an even number. (iii) will be an odd number.
25A_Q5. From a well-shuffled deck of 52 playing-cards, one card is drawn. Find the probability that the card drawn will : (i) be a black card. (ii) not be a red card. (iii) be a red card. (iv) be a face card. (v) be a face card of red colour.
25A_Q6. (i) If A and B are two complementary events then what is the relation between P(A) and P(B) ? (ii) If the probability of happening of an event A is 0.46. What will be the probability of not happening of the event A ?
25A_Q7 In a TT match between Greta and Rini the (i) winning of Geeta. (ii) not winning of Ritu.
25A_Q 8. In a race between Mahesh and John; the probability that John will lose the race is 0.54. Find the probability of : winning of Mahesh. winning of John.
25A_Q9. Write the probability of a sure event. Write the probability of an event which is impossible. (iii) For an event E, write a relation represent-ing the range of values of P(E).
25A_Q10. In a single throw of a die, find the probability of getting : (i) 5 (ii) 8 (iii) a number less than 8. (iv) a prime number.
25A_Q11. A die is thrown once. getting : (i) an even number. (ii) a number between (iii) an even number or a multiple of 3. 12. Which of the following cannot be probability of an event ? 3 (i) 3 (ii) 2.7
25A_Q Find the probability of
3 and 8.
(iii) 43% (iv) 0.6 (v) —3.2 (vi) 035
25A_Q13. A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out : (i) a white ball ?
(ii) a black ball ?
25A_Q14. A single letter is selected at random from the word 'Probability'. Find the probability that it is a vowel.
25B
EXERCISE 25(B)
25B_Q1. Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be : (i) an even number. (ii) a multiple of 3. (iii) an even number and a multiple of 3. (iv) an even number or a multiple of 3.
25B_Q2. Hundred identical cards are numbered from 1 to 100. The cards are well shuffled and then a card is drawn. Fmd the probability that the number on the card drawn is : (i) a multiple of 5. (ii) a multiple of 6. (iii) between 40 and 60. (iv) greater than 85. (v) less than 48.
25B_Q3. From 25 identical cards, numbered 1, 2, 3, 4, 5 , 24, 25; one card is drawn at random. Find the probability that the number on the card drawn is a multiple of : (i) 3 (ii) 5 (iii) 3 and 5 (iv) 3 or 5.
25B_Q4. A die is thrown once. Find the probability of getting a number : (i) less than 3. (ii) greater than or equal to 4. (iii) less than 8. (iv) greater than 6.
25B_Q5. A book contains 85 pages. A page is chosen at random. What is the probability that the sum of the digits on the page is 8 ?
25B_Q6. A pair of dice is thrown. Find the probability of getting a sum of 10 or more, if 5 appears on the first die.
Total number of cases = 6 x 6 = 36. Since favourable cases are (5, 5) and (5, 6). No. of favourable cases = 2
25B_Q7. If two coins are tossed once, what is the probability of getting : (i) 2 heads ? (ii) at least one head ? [20121 (iii) both heads or both tails ?
25B_Q 8. Two dice are rolled together. Find the probability of getting : (i) a total of at least 10. (ii) a multiple of 2 on one die and an odd number on the other die.
25B_Q 9. A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is : (i) a spade. (ii) a red card. (iii) a face card. (iv) 5 of heart or diamond. (v) lack or queen. (vi) ace and king. (vii) a red and a king. (viii) a red or a king.
25B_Q10. A bag contains 16 coloured balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is : (i) red (ii) not red (iii) white (iv) not white (v) green or red (vi) white or green (vii) green or red or white.
25B_QII. A ball is drawn at random from a box containing 12 white, 16 red and 20 green balls. Determine the probability that the ball drawn is : (i) white (ii) red (iii) not green (iv) red or white.
25B_Q12. A card is drawn from a pack of 52 cards. Find the probability that the card drawn is : (i) a red card (ii) a black card (iii) a spade (iv) an ace (v) a black ace (vi) ace of diamonds (vii) not a club (viii) a queen or a jack.
25B_Q13. Thirty identical cards are marked with numbers I to 30. If one card is drawn at random, find the probability that it is : (i) a multiple of 4 or 6. (ii) a multiple of 3 and 5. (iii) a multiple of 3 or 5.
25B_Q14. In a single throw of two dice, find the probability of : (i) a doublet (ii) a number less than 3 on each dice.
(iii) an odd number as a sum. (iv) a total of almost 10. (v) an odd number on one dice and a number less than or equal to 4 on the other dice.
EXERCISE 25(C))
25C_Q1. A bag contain 3 red balls, 4 blue balls and one yellow ball, all the balls being identical in shape and size. If a ball is taken out of the bag without looking into it; find the probability that the ball is : (i) yellow (ii) red (iii) not yellow (iv) neither yellow nor red
25C_Q 2. A dice is thrown once. What is the probability of getting a number : (i) greater than 2 ? (ii) less than or equal to 2 ?
25C_Q3. From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is : (i) a face card. (ii) not a face card. (iii) a queen of black colour. (iv) a card with number 5 or 6. (v) a card with number less than 8. (vi) a card with number between 2 and 9.
25C_Q4. In a match between A and B: (i) the probability of winning of A is 0.83. What is the probability of winning of B? (ii) the probability of losing the match is 0.49 for B. What is the probability of winning of A?
25C_Q5. A and B are friends. Ignoring the leap year, find the probability that both friends will have: (i) different birthdays. (ii) the same birthday.
25C_Q6. A man tosses two different coins (one of r 7 and another of r 51 cinviltaneouclv What
(i) at least one head ? (ii) almost one head ?
25C_Q7. A box contains 7 red balls, 8 green balls and 5 white balls. A ball is drawn at random from the box. Find the probability that the ball is : (i) white (ii) neither red nor white.
25C_Q8. All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting : (i) a black face card (ii) a queen (iii) a black card.
25C_Q 9. In a musical chairs game, a person has been advised to stop playing the music at any time within 40 seconds after its start. What is the probability that the music will stop within the first 15 seconds ?
25C_Q10 In a bundle of 50 shirts, 44 are good. 4 have minor defects and 2 have major defects. What is the probability that : (i) it is acceptable to a trader who accepts only a good shirt ? (ii) it is acceptable to a trader who rejects only a shirt with major defects ?
25C_Q11. 1\vo dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is : (i) 8 (ii) 13 (iii) less than or equal to 12.
25C_Q12. Which of the following cannot be the probability of an event ? . 3 (i) (ii) 0.82 (iii) 37% (iv) — 24
25C_Q14. A bag contains a certain number of red balls. A. ball is drawn. Find the probability that the ball drawn is : (i) black (ii) red.
25C_Q15. The probability that two boys do not have the same birthday is 0.897. What is the probability that the two boys have the same birthday ?
25C_Q 16. A bag contains 10 red balls. 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability that the ball drawn will be : (i) not red ? (ii) neither red nor green ? (iii) white or green ?
25C_Q17. A bag contains twenty 2 5 coins, fifty r 2 coins and thirty r 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin : (i) will be a r 1 coin ? (ii) will not be a r 2 coin ? (iii) will neither be a 2 5 coin nor be a Z 1 coin ?
25C_Q 18. A game consists of spinning an arrow which comes to rest pointing at one of the numbers 2, 3. 4, 5, 6, 7. 8. 9, 10. I1, 12; as shown below.
25C_QIf the outcomes are equally likely, find the probability that the pointer will point at : (i) 6 (ii) an even number. (iii) a prime number. (iv) a number greater than 8. (v) a number less than or equal to 9. (vi) a number between 3 and II.
25C_Q19. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting : (i) a queen of red colour. (ii) a black face card. (iii) the jack or the queen of hearts. (iv) a diamond. (v) a diamond or a spade.
(i) a black card. (ii) 8 of red colour. (iii) a king of black colour.
25C_Q21. Seven cards :- the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random. (i) What is the probability that the card drawn is the eight or the king ? (ii) If the king is drawn and put aside, what is the probability that the second card picked up is : (a) an ace ? (b) a king ?
22. A box contains 150 bulbs out of which 15 are defective. It is not possible to just look at a bulb and tell 25C_Qwhether or not it is defective. One bulb is taken out at random from this box. Calculate the probability that the bulb taken out is : (i) a good one (ii) a defective one.
25C_Q23. (i) 4 defective pens are accidentally mixed with 16 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is drawn at random from the lot. What is the probability that the pen is defective ? (ii) Suppose the pen drawn in (i) is defective and is not replaced. Now one more pen is drawn at random from the rest. What is the probability that this pen is : (a) defective ? (b) not defective ?
25C_Q24 A bag contains 100 identical marble stones which are numbered from 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears : (i) a perfect square number. (ii) a number divisible by 4. (iii) a number divisible by 5. (iv) a number divisible by 4 or 5. (v) a number divisible by 4 and 5.
25C_Q25. A circle with diameter 20 cm is drawn somewhere on a rectangular piece of paper with length 40 cm and width 30 cm. This paper is kept horizontal on table top and a die, very small in size, is dropped on the rectangular paper without seeing towards it. If
24. 25.
25C_Q26. Two dice (each bearing numbers I to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is : (i) 4 or 5. (ii) 7, 8 or 9. (iii) between 5 and 8. (iv) more than 10. (v) less than 6.
25C_Q 27. Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting : (i) exactly two heads. (ii) at least two heads. (iii) inmost two heads. (iv) all tails. (v) at least one tail.
25C_Q28. Two dice are thrown simultaneously. What is the probability that : (i) 4 will not come up either time ? (ii) 4 will come up at least once ?
Throwing two dice simultaneously or one dice twice give the same results.
25C_Q29. Cards marked with numbers I, 2, 3, 4, 20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is : (i) a prime number ? (ii) divisible by 3 ? (iii) a perfect square ? [2010]
25C_Q30. Offices in Delhi are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. Find the probability that they remain absent on : (i) the same day (ii) consecutive day (iii) different days.
25C_Q31. A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball; find the number of black balls in the box. 12013]
25C_Q32. From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. A card is now drawn at random.
What is the probability that the card drawn is (i) a face card (King, Jack or Queen) (ii) an even numbered red card ? 12011)
25C_Q33. A die has 6 faces marked by the given numbers as shown below :
The die is thrown once. What is the probability of getting (i) a positive integer ? (ii) an integer greater than —3 ? (iii) the smallest integer ? [2014)
25C_Q34. A bag contains 5 white balls, 6 red balls and 9 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is : (i) a green ball. (ii) a white or a red ball. (iii) neither a green ball nor a white ball. [2015[
