Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.
Step-by-Step Solution
Key Concept: Use the definition of probability for an equally likely experiment: \(P(E)=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}\). For a single toss of a fair coin, the sample space consists of two equally likely outcomes – Head (H) and Tail (T).
1. Identify the sample space\\
The possible outcomes when a coin is tossed once are: \(S = \{H, T\}\).
2. Count the total number of outcomes\\
\(n(S) = 2\).
3. Probability of getting a head\\
- Favourable outcome for event "Head" is \{H\}.
- Number of favourable outcomes \(n(H) = 1\).
- Using the definition, \[P(\text{Head}) = \frac{n(H)}{n(S)} = \frac{1}{2} = 0.5.\]
4. Probability of getting a tail\\
- Favourable outcome for event "Tail" is \{T\}.
- Number of favourable outcomes \(n(T) = 1\).
- Using the definition, \[P(\text{Tail}) = \frac{n(T)}{n(S)} = \frac{1}{2} = 0.5.\]
5. Conclusion\\
Since the coin is fair, both events are equally likely and each has probability \(\frac{1}{2}\).
Correct Answer: P(Head) = 1/2, P(Tail) = 1/2