CBSE Class 10 Maths Probability Worksheet Set 06

Question. A die is thrown once, the probability of getting a prime number is
(a) \( \frac{2}{3} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{6} \)
Answer: (c) \( \frac{1}{2} \)

Question. When four coins are tossed simultaneously, which of the following represents the sample space? 
(a) HHHH, HHHT, HHTH, HTHH, THHH, HHTT, TTHH, HTTT, THTT, TTHT, TTTH, TTTT
(b) HHHH, HHHT, HHTH, HTHH, THHH, THHT, HTTH, HTTT, THTT, TTHT, TTTH, TTTT
(c) HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT
(d) HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, HTTH, HTHT, TTHH, HTTT, THTT, TTHT, TTTH, TTTT
Answer: (c) HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT

Question. Of 50 students in a class, 16 prefer cricket, 8 prefer football, 8 prefer basketball and rest of the students prefer either tennis or hockey. There are twice as many students who prefer tennis as the number of students who prefer hockey. A student is randomly selected from the class. Which statement is correct?
(a) The probability of selecting a student who prefer hockey is more than that of selecting a student who prefer football.
(b) The probability of selecting a student who prefer tennis is more than that of selecting a student who prefer football.
(c) The probability of selecting a student who prefer hockey is more than that of selecting a student who prefer tennis.
(d) The probability of selecting a student who prefer basketball is more than that of selecting a student who prefer cricket.
Answer: (b) The probability of selecting a student who prefer tennis is more than that of selecting a student who prefer football.

Very Short Answer Questions: 

Question. In a single throw of a die, what is the probability of getting a prime number?
Answer: \( \frac{1}{2} \)

Question. A number is chosen from the numbers 1 to 50. What is the probability that the selected number is multiple of 5?
Answer: \( \frac{1}{5} \)

Question. The probability of getting a bad egg in a lot of 400 is 0.035. What is the number of bad eggs in the lot?
Answer: 14

Question. A number \( x \) is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. What is the probability that \( |x| < 2 \)?
Answer: \( \frac{3}{7} \)

Question. A bag contains 3 black marbles, 5 red marbles and 6 white marbles. If a marble is picked at random, then what is the probability that it is not a white marble?
Answer: \( \frac{4}{7} \)

Question. Avni and Arushi draws one ball each from a bag containing 2 red and 3 green balls. Avni draws a red ball first which is not put back. What is the probability that Arushi who draws next also gets a red ball?
Answer: \( \frac{1}{4} \)

Question. A letter of English alphabet is chosen at random. What is the probability that it is a letter of the word ‘MATHEMATICS’?
Answer: \( \frac{4}{13} \)

Question. A bag contains 3 red and 5 black balls. A ball is drawn at random from the bag. What is the probability that the drawn ball is not red? 
Answer: \( \frac{5}{8} \)

Short Answer Questions-I: 

Question. Two different dice are tossed together. Find the probability:
(i) of getting a doublet
(ii) of getting a sum 10, of the numbers on the two dice. 
Answer: (i) \( \frac{1}{6} \), (ii) \( \frac{1}{12} \)

Question. The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles is \( \frac{1}{5} \). The probability of selecting a black marble at random from the same jar is \( \frac{1}{4} \). If the jar contains 22 green marbles, find the total number of marbles in the jar. 
Answer: 40 marbles

Question. A die is thrown once. Find the probability of getting (i) a composite number, (ii) a prime number. 
Answer: (i) \( \frac{1}{3} \), (ii) \( \frac{1}{2} \)

Question. Cards numbered 7 to 40 were put in a box. Poonam selects a card at random. What is the probability that Poonam selects a card which is a multiple of 5?
Answer: \( \frac{7}{34} \)

Question. A bag contains 15 balls, out of which some are white and the others are black. If the probability of drawing a black ball at random from the bag is \( \frac{2}{3} \), then find how many white balls are there in the bag. 
Answer: Number of white balls = 5

Question. A card is drawn at random from a pack of 52 playing cards. Find the probability of drawing a card which is neither a spade nor a king. 
Answer: \( \frac{9}{13} \)

Question. Three different coins are tossed simultaneously. Find the probability of getting exactly one head. 
Answer: \( \frac{3}{8} \)

Question. A die is thrown once. Find the probability of getting (i) an even number (ii) an odd number.
Answer: (i) \( \frac{1}{2} \), (ii) \( \frac{1}{2} \)

Question. A pair of dice is thrown once. Find the probability of getting (i) even number on each die (ii) a total of 9. 
Answer: (i) \( \frac{1}{4} \), (ii) \( \frac{1}{9} \)

Question. A bag contains some balls of which \( x \) are white, \( 2x \) are black and \( 3x \) are red. A ball is selected at random. What is the probability that it is (i) not red? (ii) white? 
Answer: (i) \( \frac{1}{2} \), (ii) \( \frac{1}{6} \)

Question. A bag contains 6 white balls numbered 1 to 6 and 4 red balls numbered 7 to 10. Find the probability of getting a:
(a) red ball with even number on it.
(b) an odd number ball.
Answer: (a) \( \frac{1}{5} \), (b) \( \frac{1}{2} \)

Question. A card is drawn at random from a well-shuffled pack of 52 playing cards. Find the probability of getting a red face card.
Answer: \( \frac{3}{26} \)

Question. Two coins are tossed simultaneously. What is the probability of getting at least one head?
Answer: \( \frac{3}{4} \)

Question. What is the probability of getting atmost one tail when two coins are tossed simultaneously?
Answer: \( \frac{3}{4} \)

Question. A letter of English alphabet is chosen at random. Determine the probability that the letter is a consonant.
Answer: \( \frac{21}{26} \)

Question. If probability of success is 63%, what is the probability of failure?
Answer: 37%

Question. There are 30 cards of same size in a bag on which the numbers 1 to 30 are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by 3.
Answer: \( \frac{2}{3} \)

Question. In a simultaneous throw of a pair of dice, find the probability of getting a doublet of even numbers.
Answer: \( \frac{1}{12} \)

Question. A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.
Answer: \( \frac{2}{25} \)

Question. Two different dice are rolled simultaneously. Find the probability that the sum of numbers appearing on the two dice is 10. 
Answer: \( \frac{1}{12} \)

Question. Two different dice are tossed together. Find the probability:
(i) that the number on each die is even.
(ii) that the sum of numbers appearing on the two dice is 5. 
Answer: (i) \( \frac{1}{4} \), (ii) \( \frac{1}{9} \)

Short Answer Questions-II: 

Question. Two dice are thrown simultaneously. Find the probability of getting the sum 
(i) 9.
(ii) 1.
(iii) a prime number.
Answer: (i) \( \frac{1}{9} \), (ii) 0, (iii) \( \frac{5}{12} \)

Question. Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is: 
(i) 0.
(ii) 2.
Answer: (i) \( \frac{1}{6} \), (ii) \( \frac{2}{9} \)

Question. Two different dice are thrown together. Find the probability that the product of the numbers appeared is less than 18.
Answer: \( \frac{13}{18} \)

Question. A die has its six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total score is recorded. 
(i) How many different scores are possible?
(ii) What is the probability of getting a total of 7?
Answer: (i) 6, (ii) \( \frac{1}{3} \)

Question. A bag contains white, black and red balls only. A ball is drawn at random from the bag. The probability of getting a white ball is \( \frac{3}{10} \) and that of a black ball is \( \frac{2}{5} \). Find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.
Answer: \( \frac{3}{10} \), 50 balls

Question. A die is thrown twice. What is the probability that:
(i) 3 will not come up either time?
(ii) 3 will come up at least once?
Answer: (i) \( \frac{25}{36} \), (ii) \( \frac{11}{36} \)

Question. A bag contains 8 red, 7 orange and 9 green balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is:
(i) orange or green.
(ii) not orange.
(iii) neither green nor red.
Answer: (i) \( \frac{2}{3} \), (ii) \( \frac{17}{24} \), (iii) \( \frac{7}{24} \)

Question. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a black card nor a king.
Answer: \( \frac{6}{13} \)

Question. All the jacks, queens and kings are removed from a deck of 52 playing cards and then well shuffled. Then one card is drawn at random. If an ace is given a value 1, find the probability that the card has a value:
(i) 5.
(ii) less than 5.
(iii) greater than 5.
Answer: (i) \( \frac{1}{10} \), (ii) \( \frac{2}{5} \), (iii) \( \frac{1}{2} \)

Question. A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears:
(i) a single digit number.
(ii) a number which is a perfect square.
Answer: (i) \( \frac{8}{89} \), (ii) \( \frac{8}{89} \)

Question. A carton of 24 bulbs contain 6 defective bulbs. One bulb is drawn at random. What is the probability that the bulb is not defective? If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective? 
Answer: \( P(\text{not defective}) = \frac{3}{4} \), \( P(\text{2nd bulb defective}) = \frac{5}{23} \)

Question. A child’s game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a: 
(i) triangle.
(ii) square.
(iii) square of blue colour.
(iv) triangle of red colour.
Answer: (i) \( \frac{4}{9} \), (ii) \( \frac{5}{9} \), (iii) \( \frac{1}{3} \), (iv) \( \frac{5}{18} \)

Question. Box \( a \) contains 25 slips of which 19 are marked Rs. 1 and other are marked Rs. 5 each. Box \( b \) contains 50 slips of which 45 are marked Rs. 1 each and others are marked Rs. 13 each. Slips of both the boxes are poured into a third box and reshuffled. A slip is drawn at random. What is the probability that it is marked other than Rs. 1? 
Answer: \( \frac{11}{75} \)

Question. A lot of 60 bulbs contain 12 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective? Suppose the bulb drawn in first attempt is 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: \( \frac{1}{5}, \frac{48}{59} \)

Long Answer Questions: 

Question. The King, Queen and Jack of clubs are removed from a pack of 52 cards and then the remaining cards are well shuffled. A card is selected from the remaining cards. Find the probability of getting a card
(i) of spade
(ii) of black king
(iii) of club
(iv) of jacks
Answer: (i) \( \frac{13}{49} \), (ii) \( \frac{1}{49} \), (iii) \( \frac{10}{49} \), (iv) \( \frac{3}{49} \)

Question. The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is \( \frac{1}{4} \). The probability of selecting a white marble at random from the same jar is \( \frac{1}{3} \). If this jar contains 10 yellow marbles, what is the total number of marbles in the jar?
Answer: 24

Question. Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is: 
(i) a king.
(ii) of red colour.
(iii) a face card.
(iv) a queen.
Answer: (i) \( \frac{1}{12} \), (ii) \( \frac{1}{2} \), (iii) \( \frac{1}{6} \), (iv) \( \frac{1}{24} \)

Question. Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is:
(i) not divisible by 3.
(ii) a prime number greater than 7.
(iii) not a perfect square number.
Answer: (i) \( \frac{2}{3} \), (ii) \( \frac{1}{5} \), (iii) \( \frac{5}{6} \)