PYQ Collection:
Unique questions extracted from Series 30/1 to 30/6.
Repeated questions have been consolidated while retaining all
relevant Series and Question references.
Section A — Multiple Choice Questions (1 Mark)
A card is selected at random from a deck of 52 playing cards.
The probability of it being a red face card is:
(A) \(\frac{3}{13}\)
(B) \(\frac{2}{13}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{3}{26}\)
A card is drawn at random from a pack of 52 cards.
What is the probability that the card drawn is a spade or a king?
(A) \(\frac{1}{13}\)
(B) \(\frac{2}{13}\)
(C) \(\frac{4}{13}\)
(D) \(\frac{9}{13}\)
The probability of drawing an even prime number out of numbers
from 1 to 30 is:
(A) \(\frac{1}{30}\)
(B) \(\frac{4}{15}\)
(C) \(\frac{7}{30}\)
(D) 0
In a cricket match, a batsman hits the boundary 7 times out of
the 42 balls he plays. The probability of his
not hitting a boundary is:
(A) \(\frac{1}{7}\)
(B) \(\frac{2}{7}\)
(C) \(\frac{5}{6}\)
(D) \(\frac{1}{6}\)
If all the red face cards are removed from the deck of 52 playing
cards, then the probability of getting a black jack from the
remaining cards is:
(A) \(\frac{2}{46}\)
(B) \(\frac{2}{52}\)
(C) \(\frac{4}{48}\)
(D) \(\frac{2}{23}\)
If for any event \(E\),
\(P(E)+P(\overline{E})=q\), then the value of
\(q^2-3\) is:
A die is thrown once. The probability of getting a number which
is not a factor of 36, is:
(A) \(\frac{1}{2}\)
(B) \(\frac{2}{3}\)
(C) \(\frac{1}{6}\)
(D) \(\frac{5}{6}\)
If in a lottery, there are 10 prizes and 30 blanks, then the
probability of winning a prize is:
(A) \(\frac{1}{4}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{3}{4}\)
(D) \(\frac{2}{3}\)
The number of red balls in a bag is 10 more than the number of
black balls. If the probability of drawing a red ball at random
from this bag is \(\frac{3}{5}\), then the total number of balls
in the bag is:
(A) 50
(B) 60
(C) 80
(D) 40
A pair of dice is thrown. The probability that the sum of numbers
appearing on top faces is at most 10 is:
(A) \(\frac{1}{11}\)
(B) \(\frac{10}{11}\)
(C) \(\frac{5}{6}\)
(D) \(\frac{11}{12}\)
A pair of dice is thrown once. The probability that the sum of
numbers appearing on top faces is at least 4 is:
(A) \(\frac{1}{11}\)
(B) \(\frac{10}{11}\)
(C) \(\frac{5}{6}\)
(D) \(\frac{11}{12}\)
The probability of getting a composite number greater than 3
on throwing a die is:
(A) \(\frac{1}{6}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{2}{3}\)
A piggy bank contains ₹1 coins and ₹2 coins in the ratio
\(9:11\) respectively. The piggy bank is accidentally dropped
and a coin pops out of it. The probability that it is a ₹2 coin is:
(A) \(\frac{9}{11}\)
(B) 0.45
(C) 0.55
(D) \(\frac{1}{11}\)
A bag contains red coloured, blue coloured and green coloured
balls in the ratio \(2:3:4\). A ball is drawn at random from the
given bag. The probability that the ball so drawn is
not of blue colour is:
(A) \(\frac{1}{9}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{2}{3}\)
(D) \(\frac{5}{9}\)
Two coins are tossed simultaneously. The probability of getting
at least one head is:
(A) \(\frac{1}{4}\)
(B) \(\frac{1}{2}\)
(C) \(\frac{3}{4}\)
(D) 1
Assertion–Reason Questions (1 Mark)
Assertion (A):
The probability of selecting a number at random from the numbers
1 to 20 is 1.
Reason (R):
For any event \(E\), if \(P(E)=1\), then \(E\) is called a
sure event.
Assertion (A):
In an experiment of throwing a die, Event \(E_1\): getting a
number less than 3 and Event \(E_2\): getting a number greater
than 3 are complementary events.
Reason (R):
If two events \(E\) and \(F\) are complementary events, then
\(P(E)+P(F)=1\).
Section B — Very Short Answer Questions (2 Marks)
The probability of guessing the correct answer of a certain test
question is \(\frac{x}{12}\). If the probability of not guessing
the correct answer is \(\frac{5}{6}\), then find the value of \(x\).
Two friends Anil and Ashraf (or Saima and Aryaa) were born in the
month of December in the year 2010. Find the probability that:
(i) They share the same date of birth.
(ii) They have different dates of birth.
Renu and Simran both were born in the year 2000, which is a leap
year. Find the probability that:
(i) They share the same date of birth.
(ii) They have different dates of birth.
While shuffling a pack of 52 cards, one card was accidentally
dropped. Find the probability that the dropped card:
(i) is not a face card.
(ii) is a black king.
All the face cards are removed from the pack of 52 cards and a
card is drawn at random from the remaining cards. Find the
probability that the card so drawn is:
(i) a spade.
(ii) not an ace.
From a pack of 52 cards, all aces and all kings are removed.
A card is drawn at random from the remaining cards. Find the
probability that the card so drawn is:
(i) a face card.
(ii) a card of red colour.
The number of red balls in a bag is three more than the number of
black balls. If the probability of drawing a red ball at random
from the given bag is \(\frac{12}{23}\), find the total number
of balls in the given bag.
A bag contains balls numbered 2 to 91 such that each ball bears
a different number. A ball is drawn at random from the bag.
Find the probability that:
(i) It bears a 2-digit number.
(ii) It bears a multiple of 1.
Section C — Short Answer Questions (3 Marks)
Two dice are thrown at the same time. Determine the probability
that the difference of the numbers on the two dice is 2.
Two dice are rolled together. Find the probability of getting:
(i) a multiple of 2 on one and a multiple of 3
on the other die.
(ii) the product of two numbers on the top of
the two dice is a perfect square.
Three unbiased coins are tossed simultaneously. Find the
probability of getting:
(a) exactly two tails
(b) at least one head
(c) at most two heads
If 65% of the population has black eyes, 25% have brown eyes and
the remaining have blue eyes, what is the probability that a
person selected at random has:
(a) blue eyes?
(b) brown or black eyes?
All face cards of spades are removed from a pack of 52 playing
cards and the remaining pack is shuffled well. A card is then
drawn at random from the remaining pack. Find the probability
of getting:
(a) a face card
(b) an ace or a jack
Section E — Case Study Based Questions (4 Marks)
Rahul's Lucky Charm
Rahul has a jar of cards numbered from 10 to 74.
Rules:
• Even number = Win.
• Even and divisible by 5 = Win by a big margin.
• Odd number less than 30 = Win by a small margin.
• Prime number between 50 and 74 = Lose.
(i)
What is the probability that Rahul draws a card with an even
number? (1 Mark)
(ii)
What is the probability that Rahul draws a card with an odd
number less than 30? (1 Mark)
(iii) (a)
What is the probability that Rahul draws a card with a prime
number between 50 and 74? (2 Marks)
OR
(iii) (b)
What is the probability that Rahul draws a card with an even
number divisible by 5? (2 Marks)
End of Chapter 14 — Probability
Total Unique Questions:
31
MCQs: 15 |
Assertion–Reason: 2 |
2 Marks: 8 |
3 Marks: 5 |
Case Study: 1