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

To solve this problem, we need to understand the total number of outcomes and the favorable outcomes.

Step 1: Total Outcomes When a coin is tossed three times, the total number of outcomes is 2^3 = 8. This is because each toss has 2 possible outcomes (heads or tails), and we have 3 tosses.

Step 2: Favorable Outcomes The favorable outcomes are the ones where no two successive tosses show the same face. These are HTH and THT. So, there are 2 favorable outcomes.

Step 3: Probability Calculation The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes. So, the probability that no two successive tosses show the same face is 2/8 = 1/4 or 0.25.

So, the probability that no two successive tosses show the same face when a coin is tossed three times is 0.25 or 25%.