Question 26 of 55beginner🔧 ApplyShort Answer2 marks

A coin is tossed twice, what is the probability that at least one tail occurs?

Correct Answer

When a coin is tossed twice, the possible outcomes are: (H, H), (H, T), (T, H), (T, T). These are all equally likely outcomes.

The outcomes favourable to the event 'at least one tail' are (H, T), (T, H) and (T, T). So, the number of favourable outcomes is 3. Therefore, P(at least one tail) = 3/4. Alternatively, P(at least one tail) = 1 – P(no tail) = 1 – P(H, H) = 1 – 1/4 = 3/4.

Exercise: EXERCISE 14.2 | Q: 2 | (Page Page 17)
For More Understanding

Explanation

This question mirrors Example 9 from the textbook, which calculates probability of 'at least one head'. The same logic applies: total outcomes = 4, favourable outcomes for 'at least one tail' = 3 (all except H,H). The complement method is also shown in the textbook as a valid alternative approach.

Solution Steps

  1. Step 1: List all possible outcomes when coin is tossed twice: (H,H), (H,T), (T,H), (T,T) — Total = 4

  2. Step 2: Identify favourable outcomes for 'at least one tail': (H,T), (T,H), (T,T) — Count = 3

  3. Step 3: Calculate probability = Favourable outcomes / Total outcomes = 3/4

PreviousNext