The probability of an impossible event is:
- ✓$0$
- B$1$
- C$\frac{1}{2}$
- DNon-existent.
Answer: A.
View full solution →Question types
Probability question types
326 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
326
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
111 Q→02Assertion (A) & Reason (B) MCQ
7 Q→03Fill In The Blanks[1 Marks ]
31 Q→041 Marks Question
55 Q→052 Marks Questions
65 Q→063 Marks Question
22 Q→075 Marks Questions
25 Q→08Case study (4 Marks)
10 Q→Sample Questions
Probability questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. The probability that the number on this card is divisible by both 2 and 3 is:
- A$\frac{1}{5}$
- B$\frac{3}{25}$
- ✓$\frac{4}{25}$
- D$\frac{2}{25}$
Answer: C.
View full solution →Two dice are rolled simultaneously. The probability that they show different faces is:
- A$\frac{2}{3}$
- B$\frac{1}{6}$
- C$\frac{1}{3}$
- ✓$\frac{5}{6}$
Answer: D.
View full solution →A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is:
- A$\frac{1}{4}$
- B$\frac{1}{3}$
- C$\frac{4}{9}$
- ✓$\frac{7}{9}$
Answer: D.
View full solution →In a single throw of a die, the probability of getting a multiple of 3 is:
- A$\frac{1}{2}$
- ✓$\frac{1}{3}$
- C$\frac{1}{6}$
- D$\frac{2}{3}$
Answer: B.
View full solution →Statement-1 (A): In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does hit the boundary is $\frac{4}{5}$.
Statement-2 (R): P(E) + P(notE) = 1
Statement-2 (R): P(E) + P(notE) = 1
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-7
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): Avni and Manvi were born in the year 2000. The probability that they have the same birthday is $\frac{1}{366}$.
Statement-2 (R): Leap year has 366 days.
Statement-2 (R): Leap year has 366 days.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-6
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): A four digit number is formed using the digits 1, 2, 5, 6 and 8 without repetition. The probability that it is an even number is $\frac{3}{5}$.
Statement-2 (R): The units digit of even number is also an even number.
Statement-2 (R): The units digit of even number is also an even number.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-5
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: B.
View full solution →Statement-1 (A): A number is selected from the numbers 1, 2, 3, ..., 10. The probability that it is a root of the equation$x^2-2 x+1=0$ is $\frac{1}{5}$.
Statement-2 (R): The equation $x^2-2 x+1=0$ has two roots
Statement-2 (R): The equation $x^2-2 x+1=0$ has two roots
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-4
- CStatement-1 is true, Statement-2 is false.
- ✓Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →Statement-1 (A): A cubical die is rolled. The probability of getting a composite number is $\frac{1}{3}$.
Statement-2 (R): In a throw of a cubical die, the probability of getting a prime number is $\frac{2}{3}$.
Statement-2 (R): In a throw of a cubical die, the probability of getting a prime number is $\frac{2}{3}$.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-3
- ✓Statement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: C.
View full solution →Sum of the probabilities of each outcome in an experiment is ____________ .
A letter of English alphabets is chosen at random. The probability that it is a consonant is ____________ .
A die has its six faces marked 0, 1, 1, 1, 6, 6. If two such dice are thrown together, then the probability of getting a total of 7 is ____________ .
A box contains 5 apples, 6 oranges and 'x' bananas. If the probability of selecting an apple from the box is $1 / 3$ then the number of bananas is ____________ .
View full solution →Two numbers 'a' and 'b' are selected, successively without replacement in that order, from integers 1 to 10. The probability that a/b is an integer, is ____________ .
In a simultaneous throw of pair of dice, find the probability of getting:
A doublet of odd numbers.
A doublet of odd numbers.
In a simultaneous throw of pair of dice, find the probability of getting:A sum greater than 9.
In a simultaneous throw of pair of dice, find the probability of getting:
At least once.
At least once.
In a simultaneous throw of pair of dice, find the probability of getting:
A doublet.
A doublet.
In a simultaneous throw of pair of dice, find the probability of getting:
A sum more than 7.
A sum more than 7.
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:
A heart.
A heart.
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:
- Divisible by 2 or 3.
- A prime number.
A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:
Jack.
Jack.
Examine each of the following statements and comment:
If a die in thrown once, there are two possible outcomes - an odd number or an even number. Therefore, the probability of obtaining an odd number is $\frac{1}{2}$ and the probability of obtaining an even number is $\frac{1}{2}$.
View full solution →If a die in thrown once, there are two possible outcomes - an odd number or an even number. Therefore, the probability of obtaining an odd number is $\frac{1}{2}$ and the probability of obtaining an even number is $\frac{1}{2}$.
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:
- Red.
- Black.
A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person form the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is:
- Extremely patient.
- Extremely kind or honest.
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:
- Red?
- White?
- Not green?
In the figure, a square dart board is shown. The length of a side of the larger square is $1.5$ times the length of a side of the smaller square. If a dart is thrown and lands on the larger square. What is the probability that it will land in the interior of the smaller square?
View full solution →Suppose you drop a tie at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1m?
A piggy bank contains hundred 50 paise coins, fifity ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which fell:
- Will be a 50 paise coin.
- Will be of value more than ₹1.
- Will be of value less than ₹5.
- Will be a ₹1 or ₹2 coin.
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:
- Not divisible by 3.
- A prime number great than 7.
- Not a perfect square number.
Cards marked with numbers 13, 14, 15, ....., 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the card drawn is:
- Divisible by 5.
- A number is a perfect square.
A bag contains 6 red balls and some blue balls. if the probability of a drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.
All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability to getting a:
- Face card.
- Red card.
- Black card.
- King.
Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had.
One school is chosen at random. Then:
(i) Find the probability that the school chosen at random has more than 100 computers.
(ii) Find the probability that the school chosen at random has 50 or fewer computers.
(iii) Find the probability that the school chosen at random has not more than 20 computers.
(iv) Find the probability that the school chosen at random has 10 or less than 10 computers.
| Number of Computers | 1-10 | 11-20 | 21-50 | 51-100 | 101 and more |
| Number of Schools | 250 | 200 | 290 | 180 | 80 |
One school is chosen at random. Then:
(i) Find the probability that the school chosen at random has more than 100 computers.
(ii) Find the probability that the school chosen at random has 50 or fewer computers.
(iii) Find the probability that the school chosen at random has not more than 20 computers.
(iv) Find the probability that the school chosen at random has 10 or less than 10 computers.
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