NIMCET 2010 — Mathematics PYQ

Solution

1. Determine the Total Number of Outcomes

When a fair coin is tossed, there are 2 possible outcomes for each toss: Head (H) or Tail (T). For three tosses, the total number of outcomes in the sample space $S$ is:

The sample space is:

2. Identify the Favorable Outcomes

The question asks for the probability of getting heads and tails alternatively. This means no two identical results can be next to each other.

The favorable outcomes are:

• Head, Tail, Head $\to (HTH)$

• Tail, Head, Tail $\to (THT)$

So, the number of favorable outcomes $n(E)$ is:

3. Calculate the Probability

The probability $P(E)$ is given by the ratio of favorable outcomes to total outcomes:

Simplify the fraction:

Correct Option:

The correct option is (d) $\frac{1}{4}$.