Question

If a coin is tossed three times, what is the probability that NO two successive tosses show the same face?

• A. 0.25
• B. 0.33
• C. 0.20
• D. 0.125

Hint:

When tossing a coin multiple times, list all possible outcomes to calculate the favorable ones.

Answer 1

The Correct Option is A

Step 1: Understanding the problem. 
We are tossing a coin three times and need the probability that NO two successive tosses show the same face. The possible sequences of tosses are: - HTH, THT (both have no successive tosses with the same face). 
 

Step 2: Analyzing the total number of possible outcomes. 
The total number of possible outcomes for three tosses of a coin is \( 2^3 = 8 \). The possible sequences are: HTH, THT, HHH, TTT, HHT, HTT, THH, TTH. 
 

Step 3: Calculating favorable outcomes. 
The favorable outcomes are HTH and THT. Therefore, the number of favorable outcomes is 2. 
 

Step 4: Calculating probability. 
The probability is the ratio of favorable outcomes to total outcomes: \[ P = \frac{2}{8} = 0.25. \]

Step 5: Conclusion. 
The correct answer is (A) 0.25.