Class 10 Maths: Simple Probability Previous Year Questions

CBSE 2023 • 2 Marks Question 1

Step-by-Step Solution:

The sample space when a die is thrown is \(S = \{1, 2, 3, 4, 5, 6\}\). Total possible outcomes \(n(S) = 6\).

(i) Prime numbers are \(\{2, 3, 5\}\). Favourable outcomes \(m = 3\).
\(P(\text{prime}) = \frac{m}{n} = \frac{3}{6} = \frac{1}{2}\).

(ii) Numbers greater than 4 are \(\{5, 6\}\). Favourable outcomes \(m = 2\).
\(P(> 4) = \frac{2}{6} = \frac{1}{3}\).
Answers: (i) 1/2, (ii) 1/3.

CBSE 2020 • 2 Marks Question 2

Step-by-Step Solution:

When two coins are tossed, the sample space is:
\(S = \{HH, HT, TH, TT\}\). Total outcomes \(= 4\).
Outcomes with at least one head (1 or 2 heads) are \(\{HH, HT, TH\}\). Number of favourable outcomes \(= 3\).
\(P(\text{at least one head}) = \frac{3}{4}\).
Answer: 3/4.

CBSE 2019 • 3 Marks Question 3

Step-by-Step Solution:

Let the number of blue balls be \(x\).
Total number of balls \(= 5 + x\).
\(P(\text{Red}) = \frac{5}{5 + x}\) and \(P(\text{Blue}) = \frac{x}{5 + x}\).
According to the question: \(P(\text{Blue}) = 3 \times P(\text{Red})\)
\(\frac{x}{5 + x} = 3 \times \frac{5}{5 + x} \implies x = 15\).
Answer: The number of blue balls is 15.