NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3

Question 24

Step 1: Write all possible outcomes.

When a coin is tossed 2 times, the possible outcomes are:

• HH (first toss Head, second toss Head)
• HT (first toss Head, second toss Tail)
• TH (first toss Tail, second toss Head)
• TT (first toss Tail, second toss Tail)

So, the total number of outcomes = 4.

Step 2: Understand the condition "at most one head".

"At most one head" means we can have 0 heads or 1 head. It cannot be more than 1.

Step 3: Find the favourable outcomes.

• 0 heads → TT
• 1 head → HT, TH

So favourable outcomes = TT, HT, TH (total 3 outcomes).

Step 4: Apply probability formula.

\( P(E) = \dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} \)

\( P(E) = \dfrac{3}{4} \)

Final Answer: \(\dfrac{3}{4}\)