Question

What is the probability of getting a head and a tail in a toss of two coins ?

• A. 0
• B. 1
• C. 0.25
• D. 0.5

Hint:

Be careful with the wording: "getting a head and a tail" implies exactly one of each. If the question asked for "at least one head", the favorable set would be \( \{HH, HT, TH\} \) with a probability of \( 0.75 \).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes in a defined sample space.
Key Formula or Approach:
For a sample space \( S \) and an event \( E \):
\[ P(E) = \frac{n(E)}{n(S)} \]

Step 2: Detailed Explanation:
When two unbiased coins are tossed, the sample space \( S \), representing all possible outcomes, is:
\[ S = \{HH, HT, TH, TT\} \]
where \( H \) represents Head and \( T \) represents Tail.
The number of total outcomes is:
\[ n(S) = 4 \]
The event \( E \) is defined as "getting a head and a tail", which means getting exactly one head and one tail regardless of the order.
The outcomes that satisfy this condition are \( HT \) (first coin Head, second coin Tail) and \( TH \) (first coin Tail, second coin Head).
Therefore, the favorable event set is:
\[ E = \{HT, TH\} \]
The number of favorable outcomes is:
\[ n(E) = 2 \]
Using the probability formula:
\[ P(E) = \frac{n(E)}{n(S)} = \frac{2}{4} = 0.5 \]

Step 3: Final Answer:
The probability of getting a head and a tail is 0.5.