CBSE Class 10 Maths Probability Worksheet Set 07

SECTION A

Question. Choose and write the correct option in the following questions. 
(i) A bag contains 3 red balls, 5 white balls and 7 black balls. What is the probability that a ball drawn from the bag at random will be neither red nor black?
(a) \( \frac{1}{5} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{7}{15} \)
(d) \( \frac{8}{15} \)
Answer: (b) \( \frac{1}{3} \)

Question. When a die is thrown, the probability of getting an even number less than 4 is
(a) \( \frac{1}{4} \)
(b) 0
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{6} \)
Answer: (d) \( \frac{1}{6} \)

Question. Which of the following can be the probability of an event?
(a) – 0.04
(b) 1.004
(c) \( \frac{18}{23} \)
(d) \( \frac{8}{7} \)
Answer: (c) \( \frac{18}{23} \)

Question. Solve the following questions.
(i) In a game, a number is chosen at random from the set 1, 2, 3, ...28, 29, 30. What is the probability that the number chosen is a product of exactly two different prime numbers?
(ii) The probability of getting a bad egg from a lot of 500 eggs is 0.028. What is the number of bad eggs?
Answer: (i) \( \frac{7}{30} \) (ii) 14

SECTION B

Question. Solve the following questions.
Find the probability that a number selected from the numbers 1 to 25 is not a prime number when each of the given numbers is equally likely to be selected.
Answer: \( \frac{16}{25} \)

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 dice are thrown at the same time. Find the probability of getting:
(i) same number on both dice.
(ii) different numbers on both dice.
Answer: (i) \( \frac{1}{6} \) (ii) \( \frac{5}{6} \)

Question. A coin is tossed 2 times. List the possible outcomes. Find the probability of getting:
(i) at least one head.
(ii) atmost one head.
Answer: Possible outcomes are {HH, HT, TH, TT}; (i) \( \frac{3}{4} \) (ii) \( \frac{3}{4} \)

Question. Solve the following questions.
The king, queen and jack of clubs are removed from a deck of 52 cards. The remaining cards are mixed together and then a card is drawn at random from it. Find the probability of getting
(i) a face card
(ii) a card of heart
(iii) a card of clubs
(iv) a queen of diamond
Answer: (i) \( \frac{9}{49} \) (ii) \( \frac{13}{49} \) (iii) \( \frac{10}{49} \) (iv) \( \frac{1}{49} \)

Question. A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.
Answer: 45

Question. A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is
(i) divisible by 2 or 3.
(ii) a prime number.
Answer: (i) \( \frac{13}{20} \) (ii) \( \frac{2}{5} \)

Question. In a game, the entry fee is Rs. 5. The game consists of tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she shows 3 heads, she receives double the entry fees. Otherwise, she will lose. After tossing a coin three times, find the probability that she:
(i) loses the entry fee.
(ii) gets double entry fee.
(iii) just gets her entry fee.
Answer: (i) \( \frac{1}{8} \) (ii) \( \frac{1}{8} \) (iii) \( \frac{3}{4} \)

Question. Solve the following questions. 
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 number divisible by 5. 
Answer: (i) \( \frac{9}{10} \) (ii) \( \frac{1}{5} \)

Question. Cards, on which numbers 1, 2, 3, .........., 100 are written (one number on one card and no number is repeated) are put in a bag and are mixed thoroughly. A card is drawn at random from the bag. Find the probability that card taken out has
(i) an even number
(ii) a number which is a multiple of 13
(iii) a perfect square number
(iv) a prime number less than 20
Answer: (i) \( \frac{1}{2} \) (ii) \( \frac{7}{100} \) (iii) \( \frac{1}{10} \) (iv) \( \frac{2}{25} \)

Question. A dice is rolled twice. Find the probability that:
(i) 5 will not come up either time.
(ii) 5 will come up exactly one time. 
Answer: (i) \( \frac{25}{36} \) (ii) \( \frac{5}{18} \)