Harpreet tosses two different coins simultaneously (say, one is of ` 1 and other of ` 2). What is the probability that she gets at least one head?
Step-by-Step Solution
Key Concept: Use the classical definition of probability: when all outcomes are equally likely, \(P(E)=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}\). For two independent coin tosses, list all possible ordered outcomes.
1. Identify the sample space (S).
Since the two coins are different, each toss can give a head (H) or a tail (T). The ordered pairs are:
$$S = \{(H_1,H_2),\;(H_1,T_2),\;(T_1,H_2),\;(T_1,T_2)\}$$
Hence, \(|S| = 4\).
2. Determine the favourable outcomes.
The event "at least one head" includes all outcomes except the one where both are tails:
$$E = \{(H_1,H_2),\;(H_1,T_2),\;(T_1,H_2)\}$$
So, \(|E| = 3\).
3. Apply the probability formula.
$$P(\text{at least one head}) = \frac{|E|}{|S|} = \frac{3}{4}$$
4. Write the answer in simplest form.
The required probability is \(\boxed{\dfrac{3}{4}}\).
Correct Answer: 3/4