Question

A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals.

• A. \(\frac{5}{12}\)
• B. \(\frac{1}{2}\)
• C. \(\frac{5}{6}\)
• D. \(\frac{1}{6}\)

Hint:

Don't fall for the "Gambler's Fallacy." Past results of a fair coin do not make a head "due" or "less likely" on the next flip.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem tests the concept of independent events in probability. Two events are independent if the occurrence of one does not affect the probability of the other.
Step 2: Detailed Explanation:
1. A coin toss is an independent event.
2. The outcome of the fifth toss does not depend on the outcomes of the previous four tosses.
3. For a fair coin, there are two possible outcomes: Head or Tail.
4. The probability of getting a Head in any single toss is:
\[ P(H) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{2} \]
5. Therefore, despite having four consecutive tails, the probability of a head on the next toss remains \(\frac{1}{2}\).
Step 4: Final Answer:
The probability is \(\frac{1}{2}\).