Chapter-wise questions. Probability. 1. Two coins are tossed simultaneously. Find the probability of getting exactly one tail.
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1 Probability 1. Two coins are tossed simultaneously. Find the probability of getting exactly one tail cards marked with English letters A to Z (one letter on each card) are shuffled well. If one card is selected at random, what is the probability of getting a letter in the word assassination? 3. A box has 25 balls, 7 of them are red. What is the probability that the selecting a ball which is not red? 4. Two dice are thrown simultaneously. What is the probability that i) 3 will come up at both dice? ii) 3 will not come up on either of them? iii) 3 will come up on at least one? 5. A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting (a) a queen, (b) a diamond, (c) a king or an ace, and (d) a red ace. 6. Acard is drawn from an ordinary pack and a gambler bets that it is a spade of an ace. What are the odds against his winning this best? 7. A card is drawn from a well shuffled deck of playing cards. Find the probability of drawing (i) a face card, (ii) a red face card cards numbered 1,2,3,..., 16, 17 are put into a box and mixed thoroughly. One person draws a card from the box. Find the probability that the number on the cards is (i) odd, (ii) a prime, (iii) divisible by 3, and (iv) divisible by 3 and 2 both.
2 9. A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one balls is drawn at random, find the probability that it is (i) black, (ii) red, and (iii) not green. 10. A bag contains 12 balls out of which x are white. (i) If one ball is drawn at random, what will be the probability that it will be a white ball? (ii) If 6 more white balls are put into the bag, the probability of drawing a white ball? II) If 6 more white balls are put into the bag, the probability of drawing a white ball will double than that in (i). Find X. 11. It is known that a box of 600 electric bulbs contains 12 defective bulbs. One bulb is taken out at random from this box. What is the probability that it is a non-defective bulb? 12. Three coins are tossed simultaneously. Write the sample space. Also find the probability of getting (a) all heads, (b) not more than one head, and (c) two heads. 13. A dice is thrown twice. Write the sample space. Find the probability of (i) doublets, (ii) prime number on each die, (iii) getting a total of From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen. 15. One letter is selected at random from the word Association. Find the probability of selecting O 16. In a throw of a pair of dice, what is the probability of getting a sum more than 9? 17. A box has 30 counters in it. 6 of the counters are yellow. You take one counter out of the box at random. What is the probability that the counter you take out is not yellow?
3 cards marked with English alphabets come letter on each cards are shuffled well. If one card is selected at random, what is the probability of getting a vowel? 19. A die is thrown once. Find the probability of getting a composite or prime number. 20. What is the probability of a prime number in the factors of the number 30? 21. Two dice are thrown once, find the probability of doublets cards marked with English letters A to Z (one letter on each card) are shuffled well. If one card is selected at random, what is the probability of getting a letter in the word probability? 23. All the three face cards of diamonds are removed from a well shuffled pack of 52 cards. A card is drawn at random from the remaining pack. Find the probability of getting a red face card? 24. All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is drawn at random from the remaining pack. Find the probability of getting (a) a black face card b) a queen c) a black card 25. A die is thrown once. Find the probability of getting (i) An even prime number (ii) A multiple of Cards marked with 3, 4, 5, are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the drawn card is (i) divisible by 7 (iii) A number which is a perfect square 27. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag.
4 28. An unbiased die is tossed once. Find the probability of getting (I) a multiple of 2 or 3. (II) a prime number greater than A box contains 20 balls bearing numbers 1, 2, 3, 4, A ball is drawn at random from the box. What is the probability that the number on the ball is a) an odd number b) divisible by 2 or 3. c) prime number d) not divisible by A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn is i) A card of spades or an ace ii) A red king iii) Either a king or a queen iv) Neither a king nor a queen 31. A bag contains 3 red, 5 black and 7 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is (i) white (ii) red (iii) not black (iv) red or white 32. A letter is chosen at random from the English alphabet, Find the probability that the letter chosen. a) is a vowel b) is a consonant c) precides P d) follows r/ 33. A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from the bag. What is the probability that it is. White not black 34. Three coins are tossed together. Find the probability of getting. i) exactly 2 heads ii) at least two heads iii) at least one head and one tail
5 35. A bag contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is i) white ii) red iii) not black iv) red or white 36. A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting (a) queen, (b) a diamon, (c) a king or an ace, and (d) a red ace. 37. A card is drawn from and ordinary pack and a gambler bets that it is a spade or an ace. What are the odds against his winning this bet? 38. A card is drawn from a well shuffled deck of playing cards. Find the probability of drawing (i) a face card, (ii) a red card cards numbered 1,2,3...,16,17 are put into a box and mixed thoroughly. One person draws a card from the box. Find the probability that the number on the card is (i) odd, (ii) a prime, (iii) divisible by 3, and (iv) divisible by 3 and 2 both. 40. A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls, If one ball is drawn at random, find the probability that it is (i) black, (ii) red, and (iii) not green 41. A bag contains 12 balls out of whichx are white. i) If one ball is drawn at random, what will be the probability that it will be a white ball? ii) if 6 more white balls are put into the bag, the probability of drawing a white ball will double than that in (i). Find x. 42. It is known that a box of 600 electric bulbs contains 12 defective bubls. One bulb is taken out at random from this box. What is the probability that it is a non-defective bulb?
6 43. Three coins are tossed simultaneously. Write the sample space. Also find the probability of getting (a) all heads, (b) not more than one head, and(c) tow heads. 44. A dice is thrown twice. Write the sample space. Find the probability of (i) doublets, (ii) prime number on each die, (iii) getting a total of 11.
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